NASA Astrophysics Data System (ADS)
Lloyd, Seth; Dreyer, Olaf
2016-02-01
Path integrals calculate probabilities by summing over classical configurations of variables such as fields, assigning each configuration a phase equal to the action of that configuration. This paper defines a universal path integral, which sums over all computable structures. This path integral contains as sub-integrals all possible computable path integrals, including those of field theory, the standard model of elementary particles, discrete models of quantum gravity, string theory, etc. The universal path integral possesses a well-defined measure that guarantees its finiteness. The probabilities for events corresponding to sub-integrals can be calculated using the method of decoherent histories. The universal path integral supports a quantum theory of the universe in which the world that we see around us arises out of the interference between all computable structures.
Path Integrals and Hamiltonians
NASA Astrophysics Data System (ADS)
Baaquie, Belal E.
2014-03-01
1. Synopsis; Part I. Fundamental Principles: 2. The mathematical structure of quantum mechanics; 3. Operators; 4. The Feynman path integral; 5. Hamiltonian mechanics; 6. Path integral quantization; Part II. Stochastic Processes: 7. Stochastic systems; Part III. Discrete Degrees of Freedom: 8. Ising model; 9. Ising model: magnetic field; 10. Fermions; Part IV. Quadratic Path Integrals: 11. Simple harmonic oscillators; 12. Gaussian path integrals; Part V. Action with Acceleration: 13. Acceleration Lagrangian; 14. Pseudo-Hermitian Euclidean Hamiltonian; 15. Non-Hermitian Hamiltonian: Jordan blocks; 16. The quartic potential: instantons; 17. Compact degrees of freedom; Index.
Path Integrals and Supersolids
NASA Astrophysics Data System (ADS)
Ceperley, D. M.
2008-11-01
Recent experiments by Kim and Chan on solid 4He have been interpreted as discovery of a supersolid phase of matter. Arguments based on wavefunctions have shown that such a phase exists, but do not necessarily apply to solid 4He. Imaginary time path integrals, implemented using Monte Carlo methods, provide a definitive answer; a clean system of solid 4He should be a normal quantum solid, not one with superfluid properties. The Kim-Chan phenomena must be due to defects introduced when the solid is formed.
Scattering theory with path integrals
Rosenfelder, R.
2014-03-15
Starting from well-known expressions for the T-matrix and its derivative in standard nonrelativistic potential scattering, I rederive recent path-integral formulations due to Efimov and Barbashov et al. Some new relations follow immediately.
Squeezed states and path integrals
NASA Technical Reports Server (NTRS)
Daubechies, Ingrid; Klauder, John R.
1992-01-01
The continuous-time regularization scheme for defining phase-space path integrals is briefly reviewed as a method to define a quantization procedure that is completely covariant under all smooth canonical coordinate transformations. As an illustration of this method, a limited set of transformations is discussed that have an image in the set of the usual squeezed states. It is noteworthy that even this limited set of transformations offers new possibilities for stationary phase approximations to quantum mechanical propagators.
Perturbative Methods in Path Integration
NASA Astrophysics Data System (ADS)
Johnson-Freyd, Theodore Paul
This dissertation addresses a number of related questions concerning perturbative "path" integrals. Perturbative methods are one of the few successful ways physicists have worked with (or even defined) these infinite-dimensional integrals, and it is important as mathematicians to check that they are correct. Chapter 0 provides a detailed introduction. We take a classical approach to path integrals in Chapter 1. Following standard arguments, we posit a Feynman-diagrammatic description of the asymptotics of the time-evolution operator for the quantum mechanics of a charged particle moving nonrelativistically through a curved manifold under the influence of an external electromagnetic field. We check that our sum of Feynman diagrams has all desired properties: it is coordinate-independent and well-defined without ultraviolet divergences, it satisfies the correct composition law, and it satisfies Schrodinger's equation thought of as a boundary-value problem in PDE. Path integrals in quantum mechanics and elsewhere in quantum field theory are almost always of the shape ∫ f es for some functions f (the "observable") and s (the "action"). In Chapter 2 we step back to analyze integrals of this type more generally. Integration by parts provides algebraic relations between the values of ∫ (-) es for different inputs, which can be packaged into a Batalin--Vilkovisky-type chain complex. Using some simple homological perturbation theory, we study the version of this complex that arises when f and s are taken to be polynomial functions, and power series are banished. We find that in such cases, the entire scheme-theoretic critical locus (complex points included) of s plays an important role, and that one can uniformly (but noncanonically) integrate out in a purely algebraic way the contributions to the integral from all "higher modes," reducing ∫ f es to an integral over the critical locus. This may help explain the presence of analytic continuation in questions like the
Integrated assignment and path planning
NASA Astrophysics Data System (ADS)
Murphey, Robert A.
2005-11-01
A surge of interest in unmanned systems has exposed many new and challenging research problems across many fields of engineering and mathematics. These systems have the potential of transforming our society by replacing dangerous and dirty jobs with networks of moving machines. This vision is fundamentally separate from the modern view of robotics in that sophisticated behavior is realizable not by increasing individual vehicle complexity, but instead through collaborative teaming that relies on collective perception, abstraction, decision making, and manipulation. Obvious examples where collective robotics will make an impact include planetary exploration, space structure assembly, remote and undersea mining, hazardous material handling and clean-up, and search and rescue. Nonetheless, the phenomenon driving this technology trend is the increasing reliance of the US military on unmanned vehicles, specifically, aircraft. Only a few years ago, following years of resistance to the use of unmanned systems, the military and civilian leadership in the United States reversed itself and have recently demonstrated surprisingly broad acceptance of increasingly pervasive use of unmanned platforms in defense surveillance, and even attack. However, as rapidly as unmanned systems have gained acceptance, the defense research community has discovered the technical pitfalls that lie ahead, especially for operating collective groups of unmanned platforms. A great deal of talent and energy has been devoted to solving these technical problems, which tend to fall into two categories: resource allocation of vehicles to objectives, and path planning of vehicle trajectories. An extensive amount of research has been conducted in each direction, yet, surprisingly, very little work has considered the integrated problem of assignment and path planning. This dissertation presents a framework for studying integrated assignment and path planning and then moves on to suggest an exact
Bergman Kernel from Path Integral
NASA Astrophysics Data System (ADS)
Douglas, Michael R.; Klevtsov, Semyon
2010-01-01
We rederive the expansion of the Bergman kernel on Kähler manifolds developed by Tian, Yau, Zelditch, Lu and Catlin, using path integral and perturbation theory, and generalize it to supersymmetric quantum mechanics. One physics interpretation of this result is as an expansion of the projector of wave functions on the lowest Landau level, in the special case that the magnetic field is proportional to the Kähler form. This is relevant for the quantum Hall effect in curved space, and for its higher dimensional generalizations. Other applications include the theory of coherent states, the study of balanced metrics, noncommutative field theory, and a conjecture on metrics in black hole backgrounds discussed in [24]. We give a short overview of these various topics. From a conceptual point of view, this expansion is noteworthy as it is a geometric expansion, somewhat similar to the DeWitt-Seeley-Gilkey et al short time expansion for the heat kernel, but in this case describing the long time limit, without depending on supersymmetry.
White Noise Path Integrals in Stochastic Neurodynamics
NASA Astrophysics Data System (ADS)
Carpio-Bernido, M. Victoria; Bernido, Christopher C.
2008-06-01
The white noise path integral approach is used in stochastic modeling of neural activity, where the primary dynamical variables are the relative membrane potentials, while information on transmembrane ionic currents is contained in the drift coefficient. The white noise path integral allows a natural framework and can be evaluated explicitly to yield a closed form for the conditional probability density.
Path Integral Approach to Atomic Collisions
NASA Astrophysics Data System (ADS)
Harris, Allison
2016-09-01
The Path Integral technique is an alternative formulation of quantum mechanics that is based on a Lagrangian approach. In its exact form, it is completely equivalent to the Hamiltonian-based Schrödinger equation approach. Developed by Feynman in the 1940's, following inspiration from Dirac, the path integral approach has been widely used in high energy physics, quantum field theory, and statistical mechanics. However, only in limited cases has the path integral approach been applied to quantum mechanical few-body scattering. We present a theoretical and computational development of the path integral method for use in the study of atomic collisions. Preliminary results are presented for some simple systems. Ultimately, this approach will be applied to few-body ion-atom collisions. Work supported by NSF grant PHY-1505217.
Dressed coordinates: The path-integral approach
NASA Astrophysics Data System (ADS)
Casana, R.; Flores-Hidalgo, G.; Pimentel, B. M.
2007-02-01
The recently introduced dressed coordinates are studied in the path-integral approach. These coordinates are defined in the context of a harmonic oscillator linearly coupled to massless scalar field and it is shown that in this model the dressed coordinates appear as a coordinate transformation preserving the path-integral functional measure. The analysis also generalizes the sum rules established in a previous work.
Asymptotic properties of path integral ideals
Bogojevic, A.; Balaz, A.; Belic, A.
2005-09-01
We introduce and analyze an interesting quantity, the path integral ideal, governing the flow of generic discrete theories to the continuum limit and greatly increasing their convergence. The said flow is classified according to the degree of divergence of the potential at spatial infinity. Studying the asymptotic behavior of path integral ideals we isolate the dominant terms in the effective potential that determine the behavior of a generic theory for large discrete time steps.
Local-time representation of path integrals.
Jizba, Petr; Zatloukal, Václav
2015-12-01
We derive a local-time path-integral representation for a generic one-dimensional time-independent system. In particular, we show how to rephrase the matrix elements of the Bloch density matrix as a path integral over x-dependent local-time profiles. The latter quantify the time that the sample paths x(t) in the Feynman path integral spend in the vicinity of an arbitrary point x. Generalization of the local-time representation that includes arbitrary functionals of the local time is also provided. We argue that the results obtained represent a powerful alternative to the traditional Feynman-Kac formula, particularly in the high- and low-temperature regimes. To illustrate this point, we apply our local-time representation to analyze the asymptotic behavior of the Bloch density matrix at low temperatures. Further salient issues, such as connections with the Sturm-Liouville theory and the Rayleigh-Ritz variational principle, are also discussed.
On the path integral of constrained systems
Muslih, Sami I.
2004-10-04
Constrained Hamiltonian systems are investigated by using Gueler's method. Integration of a set of equations of motion and the action function is discussed. It is shown that the canonical path integral quantization is obtained directly as an integration over the canonical phase-space coordinates without any need to enlarge the initial phase-space by introducing extra- unphysical variables as in the Batalin-Fradkin-Tyutin (BFT) method. The abelian Proca model is analyzed by the two methods.
The path integral for dendritic trees.
Abbott, L F; Farhi, E; Gutmann, S
1991-01-01
We construct the path integral for determining the potential on any dendritic tree described by a linear cable equation. This is done by generalizing Brownian motion from a line to a tree. We also construct the path integral for dendritic structures with spatially-varying and/or time-dependent membrane conductivities due, for example, to synaptic inputs. The path integral allows novel computational techniques to be applied to cable problems. Our analysis leads ultimately to an exact expression for the Green's function on a dendritic tree of arbitrary geometry expressed in terms of a set of simple diagrammatic rules. These rules providing a fast and efficient method for solving complex cable problems.
Fermionic path integrals and local anomalies
NASA Astrophysics Data System (ADS)
Roepstorff, G.
2003-05-01
No doubt, the subject of path integrals proved to be an immensely fruitful human, i.e. Feynman's idea. No wonder it is more timely than ever. Some even claim that it is the most daring, innovative and revolutionary idea since the days of Heisenberg and Bohr. It is thus likely to generate enthusiasm, if not addiction among physicists who seek simplicity together with perfection. Professor Devreese's long-lasting interest in, if not passion on the subject stems from his firm conviction that, beyond being the tool of choice, path integration provides the key to all quantum phenomena, be it in solid state, atomic, molecular or particle physics as evidenced by the impressive list of publications at the address http://lib.ua.ac.be/AB/a867.html. In this note, I review a pitfall of fermionic path integrals and a way to get around it in situations relevant to the Standard Model of particle physics.
Path Integrals on Manifolds with Boundary
NASA Astrophysics Data System (ADS)
Ludewig, Matthias
2017-09-01
We give time-slicing path integral formulas for solutions to the heat equation corresponding to a self-adjoint Laplace type operator acting on sections of a vector bundle over a compact Riemannian manifold with boundary. More specifically, we show that such a solution can be approximated by integrals over finite-dimensional path spaces of piecewise geodesics subordinated to increasingly fine partitions of the time interval. We consider a subclass of mixed boundary conditions which includes standard Dirichlet and Neumann boundary conditions.
Optical tomography with discretized path integral
Yuan, Bingzhi; Tamaki, Toru; Kushida, Takahiro; Mukaigawa, Yasuhiro; Kubo, Hiroyuki; Raytchev, Bisser; Kaneda, Kazufumi
2015-01-01
Abstract. We present a framework for optical tomography based on a path integral. Instead of directly solving the radiative transport equations, which have been widely used in optical tomography, we use a path integral that has been developed for rendering participating media based on the volume rendering equation in computer graphics. For a discretized two-dimensional layered grid, we develop an algorithm to estimate the extinction coefficients of each voxel with an interior point method. Numerical simulation results are shown to demonstrate that the proposed method works well. PMID:26839903
Optical tomography with discretized path integral.
Yuan, Bingzhi; Tamaki, Toru; Kushida, Takahiro; Mukaigawa, Yasuhiro; Kubo, Hiroyuki; Raytchev, Bisser; Kaneda, Kazufumi
2015-07-01
We present a framework for optical tomography based on a path integral. Instead of directly solving the radiative transport equations, which have been widely used in optical tomography, we use a path integral that has been developed for rendering participating media based on the volume rendering equation in computer graphics. For a discretized two-dimensional layered grid, we develop an algorithm to estimate the extinction coefficients of each voxel with an interior point method. Numerical simulation results are shown to demonstrate that the proposed method works well.
The formal path integral and quantum mechanics
Johnson-Freyd, Theo
2010-11-15
Given an arbitrary Lagrangian function on R{sup d} and a choice of classical path, one can try to define Feynman's path integral supported near the classical path as a formal power series parameterized by 'Feynman diagrams', although these diagrams may diverge. We compute this expansion and show that it is (formally, if there are ultraviolet divergences) invariant under volume-preserving changes of coordinates. We prove that if the ultraviolet divergences cancel at each order, then our formal path integral satisfies a 'Fubini theorem' expressing the standard composition law for the time evolution operator in quantum mechanics. Moreover, we show that when the Lagrangian is inhomogeneous quadratic in velocity such that its homogeneous-quadratic part is given by a matrix with constant determinant, then the divergences cancel at each order. Thus, by 'cutting and pasting' and choosing volume-compatible local coordinates, our construction defines a Feynman-diagrammatic 'formal path integral' for the nonrelativistic quantum mechanics of a charged particle moving in a Riemannian manifold with an external electromagnetic field.
The Use of Path Integral Ideals: Deriving the Euler Summation Formula for Path Integrals
Bogojevic, Aleksandar; Balaz, Antun; Belic, Aleksandar
2006-03-29
We present and comment on a new quantity that we have recently introduced: the path integral ideal. The new quantity governs the flow of a discrete quantum theory to its continuum limit. Path integral ideals satisfy a unique integral equation - the distinction between different quantum theories being in the boundary conditions. An asymptotic expansion of this equation has led to the derivation of a generalization of Euler's summation formula for path integrals. The new analytical method has brought about a systematic improvement of the convergence of path integrals. Applied to numerical procedures, the new analytical input has resulted in the speedup of numerical simulations by many orders of magnitude. On the analytical side, the integral equation for ideals may turn out to be a useful setting for extending the obtained results to a wider setting - e.g. to p-adic valued theories and theories on non-commuting space-times.
Bead-Fourier path integral molecular dynamics.
Ivanov, Sergei D; Lyubartsev, Alexander P; Laaksonen, Aatto
2003-06-01
Molecular dynamics formulation of Bead-Fourier path integral method for simulation of quantum systems at finite temperatures is presented. Within this scheme, both the bead coordinates and Fourier coefficients, defining the path representing the quantum particle, are treated as generalized coordinates with corresponding generalized momenta and masses. Introduction of the Fourier harmonics together with the center-of-mass thermostating scheme is shown to remove the ergodicity problem, known to pose serious difficulties in standard path integral molecular dynamics simulations. The method is tested for quantum harmonic oscillator and hydrogen atom (Coulombic potential). The simulation results are compared with the exact analytical solutions available for both these systems. Convergence of the results with respect to the number of beads and Fourier harmonics is analyzed. It was shown that addition of a few Fourier harmonics already improves the simulation results substantially, even for a relatively small number of beads. The proposed Bead-Fourier path integral molecular dynamics is a reliable and efficient alternative to simulations of quantum systems.
Path integration in tactile perception of shapes.
Moscatelli, Alessandro; Naceri, Abdeldjallil; Ernst, Marc O
2014-11-01
Whenever we move the hand across a surface, tactile signals provide information about the relative velocity between the skin and the surface. If the system were able to integrate the tactile velocity information over time, cutaneous touch may provide an estimate of the relative displacement between the hand and the surface. Here, we asked whether humans are able to form a reliable representation of the motion path from tactile cues only, integrating motion information over time. In order to address this issue, we conducted three experiments using tactile motion and asked participants (1) to estimate the length of a simulated triangle, (2) to reproduce the shape of a simulated triangular path, and (3) to estimate the angle between two-line segments. Participants were able to accurately indicate the length of the path, whereas the perceived direction was affected by a direction bias (inward bias). The response pattern was thus qualitatively similar to the ones reported in classical path integration studies involving locomotion. However, we explain the directional biases as the result of a tactile motion aftereffect. Copyright © 2014 Elsevier B.V. All rights reserved.
Bead-Fourier path integral molecular dynamics
NASA Astrophysics Data System (ADS)
Ivanov, Sergei D.; Lyubartsev, Alexander P.; Laaksonen, Aatto
2003-06-01
Molecular dynamics formulation of Bead-Fourier path integral method for simulation of quantum systems at finite temperatures is presented. Within this scheme, both the bead coordinates and Fourier coefficients, defining the path representing the quantum particle, are treated as generalized coordinates with corresponding generalized momenta and masses. Introduction of the Fourier harmonics together with the center-of-mass thermostating scheme is shown to remove the ergodicity problem, known to pose serious difficulties in standard path integral molecular dynamics simulations. The method is tested for quantum harmonic oscillator and hydrogen atom (Coulombic potential). The simulation results are compared with the exact analytical solutions available for both these systems. Convergence of the results with respect to the number of beads and Fourier harmonics is analyzed. It was shown that addition of a few Fourier harmonics already improves the simulation results substantially, even for a relatively small number of beads. The proposed Bead-Fourier path integral molecular dynamics is a reliable and efficient alternative to simulations of quantum systems.
A taxonomy of integral reaction path analysis
Grcar, Joseph F.; Day, Marcus S.; Bell, John B.
2004-12-23
W. C. Gardiner observed that achieving understanding through combustion modeling is limited by the ability to recognize the implications of what has been computed and to draw conclusions about the elementary steps underlying the reaction mechanism. This difficulty can be overcome in part by making better use of reaction path analysis in the context of multidimensional flame simulations. Following a survey of current practice, an integral reaction flux is formulated in terms of conserved scalars that can be calculated in a fully automated way. Conditional analyses are then introduced, and a taxonomy for bidirectional path analysis is explored. Many examples illustrate the resulting path analysis and uncover some new results about nonpremixed methane-air laminar jets.
An alternative path integral for quantum gravity
NASA Astrophysics Data System (ADS)
Krishnan, Chethan; Kumar, K. V. Pavan; Raju, Avinash
2016-10-01
We define a (semi-classical) path integral for gravity with Neumann boundary conditions in D dimensions, and show how to relate this new partition function to the usual picture of Euclidean quantum gravity. We also write down the action in ADM Hamiltonian formulation and use it to reproduce the entropy of black holes and cosmological horizons. A comparison between the (background-subtracted) covariant and Hamiltonian ways of semi-classically evaluating this path integral in flat space reproduces the generalized Smarr formula and the first law. This "Neumann ensemble" perspective on gravitational thermodynamics is parallel to the canonical (Dirichlet) ensemble of Gibbons-Hawking and the microcanonical approach of Brown-York.
Path-integral approach to lattice polarons
NASA Astrophysics Data System (ADS)
Kornilovitch, P. E.
2007-06-01
The basic principles behind a path integral approach to the lattice polaron are reviewed. Analytical integration of phonons reduces the problem to one self-interacting imaginary-time path, which is then simulated by Metropolis Monte Carlo. Projection operators separate states of different symmetry, which provides access to various excited states. Shifted boundary conditions in imaginary time enable calculation of the polaron mass, spectrum and density of states. Other polaron characteristics accessible by the method include the polaron energy, number of excited phonons and isotope exponent on mass. Monte Carlo updates are formulated in continuous imaginary time on infinite lattices and as such provide statistically unbiased results without finite-size and finite time-step errors. Numerical data are presented for models with short-range and long-range electron-phonon interactions.
Path integration: effect of curved path complexity and sensory system on blindfolded walking.
Koutakis, Panagiotis; Mukherjee, Mukul; Vallabhajosula, Srikant; Blanke, Daniel J; Stergiou, Nicholas
2013-02-01
Path integration refers to the ability to integrate continuous information of the direction and distance traveled by the system relative to the origin. Previous studies have investigated path integration through blindfolded walking along simple paths such as straight line and triangles. However, limited knowledge exists regarding the role of path complexity in path integration. Moreover, little is known about how information from different sensory input systems (like vision and proprioception) contributes to accurate path integration. The purpose of the current study was to investigate how sensory information and curved path complexity affect path integration. Forty blindfolded participants had to accurately reproduce a curved path and return to the origin. They were divided into four groups that differed in the curved path, circle (simple) or figure-eight (complex), and received either visual (previously seen) or proprioceptive (previously guided) information about the path before they reproduced it. The dependent variables used were average trajectory error, walking speed, and distance traveled. The results indicated that (a) both groups that walked on a circular path and both groups that received visual information produced greater accuracy in reproducing the path. Moreover, the performance of the group that received proprioceptive information and later walked on a figure-eight path was less accurate than their corresponding circular group. The groups that had the visual information also walked faster compared to the group that had proprioceptive information. Results of the current study highlight the roles of different sensory inputs while performing blindfolded walking for path integration.
Quantitative molecular thermochemistry based on path integrals.
Glaesemann, Kurt R; Fried, Laurence E
2005-07-15
The calculation of thermochemical data requires accurate molecular energies and heat capacities. Traditional methods rely upon the standard harmonic normal-mode analysis to calculate the vibrational and rotational contributions. We utilize path-integral Monte Carlo for going beyond the harmonic analysis and to calculate the vibrational and rotational contributions to ab initio energies. This is an application and an extension of a method previously developed in our group [J. Chem. Phys. 118, 1596 (2003)].
Quantitative Molecular Thermochemistry Based on Path Integrals
Glaesemann, K R; Fried, L E
2005-03-14
The calculation of thermochemical data requires accurate molecular energies and heat capacities. Traditional methods rely upon the standard harmonic normal mode analysis to calculate the vibrational and rotational contributions. We utilize path integral Monte Carlo (PIMC) for going beyond the harmonic analysis, to calculate the vibrational and rotational contributions to ab initio energies. This is an application and extension of a method previously developed in our group.
Systematically Accelerated Convergence of Path Integrals
Bogojevic, A.; Balaz, A.; Belic, A.
2005-05-13
We present a new analytical method that systematically improves the convergence of path integrals of a generic N-fold discretized theory. Using it we calculate the effective actions S{sup (p)} for p{<=}9, which lead to the same continuum amplitudes as the starting action, but that converge to that continuum limit as 1/N{sup p}. We checked this derived speedup in convergence by performing Monte Carlo simulations on several different models.
Fractional Levy motion through path integrals
Calvo, Ivan; Sanchez, Raul; Carreras, Benjamin A
2009-01-01
Fractional Levy motion (fLm) is the natural generalization of fractional Brownian motion in the context of self-similar stochastic processes and stable probability distributions. In this paper we give an explicit derivation of the propagator of fLm by using path integral methods. The propagators of Brownian motion and fractional Brownian motion are recovered as particular cases. The fractional diffusion equation corresponding to fLm is also obtained.
Path integration in desert ants, Cataglyphis fortis
Müller, Martin; Wehner, Rüdiger
1988-01-01
Foraging desert ants, Cataglyphis fortis, continually keep track of their own posotions relative to home— i.e., integrate their tortuous outbound routes and return home along straight (inbound) routes. By experimentally manipulating the ants' outbound trajectories we show that the ants solve this path integration problem not by performing a true vector summation (as a human navigator does) but by employing a computationally simple approximation. This approximation is characterized by small, but systematic, navigational errors that helped us elucidate the ant's way of computing its mean home vector. PMID:16593958
Breakdown of the Coherent State Path Integral: Two Simple Examples
Wilson, Justin H.; Galitski, Victor
2011-03-18
We show how the time-continuous coherent state path integral breaks down for both the single-site Bose-Hubbard model and the spin-path integral. Specifically, when the Hamiltonian is quadratic in a generator of the algebra used to construct coherent states, the path integral fails to produce correct results following from an operator approach. As suggested by previous authors, we note that the problems do not arise in the time-discretized version of the path integral.
Path integral evaluation of equilibrium isotope effects
NASA Astrophysics Data System (ADS)
Zimmermann, Tomáš; Vaníček, Jiří
2009-07-01
A general and rigorous methodology to compute the quantum equilibrium isotope effect is described. Unlike standard approaches, ours does not assume separability of rotational and vibrational motions and does not make the harmonic approximation for vibrations or rigid rotor approximation for the rotations. In particular, zero point energy and anharmonicity effects are described correctly quantum mechanically. The approach is based on the thermodynamic integration with respect to the mass of isotopes and on the Feynman path integral representation of the partition function. An efficient estimator for the derivative of free energy is used whose statistical error is independent of the number of imaginary time slices in the path integral, speeding up calculations by a factor of ˜60 at 500 K and more at room temperature. We describe the implementation of the methodology in the molecular dynamics package AMBER 10. The method is tested on three [1,5] sigmatropic hydrogen shift reactions. Because of the computational expense, we use ab initio potentials to evaluate the equilibrium isotope effects within the harmonic approximation and then the path integral method together with semiempirical potentials to evaluate the anharmonicity corrections. Our calculations show that the anharmonicity effects amount up to 30% of the symmetry reduced reaction free energy. The numerical results are compared with recent experiments of Doering et al., [J. Am. Chem. Soc. 128, 9080 (2006); J. Am. Chem. Soc.129, 2488 (2007)] confirming the accuracy of the most recent measurement on 2,4,6,7,9-pentamethyl-5-(5,5-H22)methylene-11,11a-dihydro-12H-naphthacene as well as concerns about compromised accuracy, due to side reactions, of another measurement on 2-methyl-10-(10,10-H22)methylenebicyclo[4.4.0]dec-1-ene.
Path integral quantization of generalized quantum electrodynamics
Bufalo, R.; Pimentel, B. M.; Zambrano, G. E. R.
2011-02-15
In this paper, a complete covariant quantization of generalized electrodynamics is shown through the path integral approach. To this goal, we first studied the Hamiltonian structure of the system following Dirac's methodology and, then, we followed the Faddeev-Senjanovic procedure to obtain the transition amplitude. The complete propagators (Schwinger-Dyson-Fradkin equations) of the correct gauge fixation and the generalized Ward-Fradkin-Takahashi identities are also obtained. Afterwards, an explicit calculation of one-loop approximations of all Green's functions and a discussion about the obtained results are presented.
Path integral quantization of generalized quantum electrodynamics
NASA Astrophysics Data System (ADS)
Bufalo, R.; Pimentel, B. M.; Zambrano, G. E. R.
2011-02-01
In this paper, a complete covariant quantization of generalized electrodynamics is shown through the path integral approach. To this goal, we first studied the Hamiltonian structure of the system following Dirac’s methodology and, then, we followed the Faddeev-Senjanovic procedure to obtain the transition amplitude. The complete propagators (Schwinger-Dyson-Fradkin equations) of the correct gauge fixation and the generalized Ward-Fradkin-Takahashi identities are also obtained. Afterwards, an explicit calculation of one-loop approximations of all Green’s functions and a discussion about the obtained results are presented.
High order path integrals made easy
NASA Astrophysics Data System (ADS)
Kapil, Venkat; Behler, Jörg; Ceriotti, Michele
2016-12-01
The precise description of quantum nuclear fluctuations in atomistic modelling is possible by employing path integral techniques, which involve a considerable computational overhead due to the need of simulating multiple replicas of the system. Many approaches have been suggested to reduce the required number of replicas. Among these, high-order factorizations of the Boltzmann operator are particularly attractive for high-precision and low-temperature scenarios. Unfortunately, to date, several technical challenges have prevented a widespread use of these approaches to study the nuclear quantum effects in condensed-phase systems. Here we introduce an inexpensive molecular dynamics scheme that overcomes these limitations, thus making it possible to exploit the improved convergence of high-order path integrals without having to sacrifice the stability, convenience, and flexibility of conventional second-order techniques. The capabilities of the method are demonstrated by simulations of liquid water and ice, as described by a neural-network potential fitted to the dispersion-corrected hybrid density functional theory calculations.
Building a cognitive map by assembling multiple path integration systems.
Wang, Ranxiao Frances
2016-06-01
Path integration and cognitive mapping are two of the most important mechanisms for navigation. Path integration is a primitive navigation system which computes a homing vector based on an animal's self-motion estimation, while cognitive map is an advanced spatial representation containing richer spatial information about the environment that is persistent and can be used to guide flexible navigation to multiple locations. Most theories of navigation conceptualize them as two distinctive, independent mechanisms, although the path integration system may provide useful information for the integration of cognitive maps. This paper demonstrates a fundamentally different scenario, where a cognitive map is constructed in three simple steps by assembling multiple path integrators and extending their basic features. The fact that a collection of path integration systems can be turned into a cognitive map suggests the possibility that cognitive maps may have evolved directly from the path integration system.
Path Integral Monte Carlo Methods for Fermions
NASA Astrophysics Data System (ADS)
Ethan, Ethan; Dubois, Jonathan; Ceperley, David
2014-03-01
In general, Quantum Monte Carlo methods suffer from a sign problem when simulating fermionic systems. This causes the efficiency of a simulation to decrease exponentially with the number of particles and inverse temperature. To circumvent this issue, a nodal constraint is often implemented, restricting the Monte Carlo procedure from sampling paths that cause the many-body density matrix to change sign. Unfortunately, this high-dimensional nodal surface is not a priori known unless the system is exactly solvable, resulting in uncontrolled errors. We will discuss two possible routes to extend the applicability of finite-temperatue path integral Monte Carlo. First we extend the regime where signful simulations are possible through a novel permutation sampling scheme. Afterwards, we discuss a method to variationally improve the nodal surface by minimizing a free energy during simulation. Applications of these methods will include both free and interacting electron gases, concluding with discussion concerning extension to inhomogeneous systems. Support from DOE DE-FG52-09NA29456, DE-AC52-07NA27344, LLNL LDRD 10- ERD-058, and the Lawrence Scholar program.
Path Integral Simulations of Solid ^4He
NASA Astrophysics Data System (ADS)
Ceperley, David
2006-03-01
Kim and Chan have found indications that solid ^4He is a supersolid by measuring the period of a torsional oscillator. To understand the state of solid ^4He at low temperature, we [1] have calculated tunnelling frequencies for ring exchanges in bulk solid helium with Path Integral Monte Carlo by finding the free energy of a path that begins with the atoms in one configuration and ends with a permutation of those positions. The exchange frequencies are found to be described by a lattice model which does not show superfluid behavior. However, simulations [2] of ^4He absorbed in Vycor find that ^4He forms a layered structure with the first layer solid-like and highly localized, the second layer disordered with some atoms delocalized and possibly superfluid. This persistent liquid layer mechanism can only be relevant for bulk ^4He in a very disordered crystal. New calculations [3] of the single particle density matrix, (the fourier transform of the momentum distribution) to measure ODLRA will also be discussed. [1] D. M. Ceperley and B. Bernu, Phys. Rev. Letts. 93, 155303(2004).[2] S. A. Khairallah and D. M. Ceperley, Phys. Rev. Letts. 95, 185301 (2005). [3] B. Clark and D. M. Ceperley, unpublished.
The path integral picture of quantum systems
NASA Astrophysics Data System (ADS)
Ceperley, David
2011-03-01
The imaginary time path integral ``formalism'' was introduced in 1953 by Feynman to understand the superfluid transition in liquid helium. The equilibrium properties of quantum many body systems is isomorphic to the classical statistical mechanics of cross-linking polymer-like objects. With the Markov Chain Monte Carlo method, invented by Metropolis et al., also in 1953, a potential way of calculating properties of correlated quantum systems was in place. But calculations for many-body quantum systems did not become routine until computers and algorithms had become sufficiently powerful three decades later. Once such simulations could happen, it was realized that simulations provided a deeper insight into boson superfluids, in particular the relation of bose condensation to the polymer end-to-end distance, and the superfluid density to the polymer ``winding number.'' Some recent developments and applications to supersolids, and helium droplets will be given. Finally, limitations of the methodology e.g. to fermion systems are discussed.
Polymer quantum mechanics some examples using path integrals
Parra, Lorena; Vergara, J. David
2014-01-14
In this work we analyze several physical systems in the context of polymer quantum mechanics using path integrals. First we introduce the group averaging method to quantize constrained systems with path integrals and later we use this procedure to compute the effective actions for the polymer non-relativistic particle and the polymer harmonic oscillator. We analyze the measure of the path integral and we describe the semiclassical dynamics of the systems.
Mixed time slicing in path integral simulations
NASA Astrophysics Data System (ADS)
Steele, Ryan P.; Zwickl, Jill; Shushkov, Philip; Tully, John C.
2011-02-01
A simple and efficient scheme is presented for using different time slices for different degrees of freedom in path integral calculations. This method bridges the gap between full quantization and the standard mixed quantum-classical (MQC) scheme and, therefore, still provides quantum mechanical effects in the less-quantized variables. Underlying the algorithm is the notion that time slices (beads) may be "collapsed" in a manner that preserves quantization in the less quantum mechanical degrees of freedom. The method is shown to be analogous to multiple-time step integration techniques in classical molecular dynamics. The algorithm and its associated error are demonstrated on model systems containing coupled high- and low-frequency modes; results indicate that convergence of quantum mechanical observables can be achieved with disparate bead numbers in the different modes. Cost estimates indicate that this procedure, much like the MQC method, is most efficient for only a relatively few quantum mechanical degrees of freedom, such as proton transfer. In this regime, however, the cost of a fully quantum mechanical simulation is determined by the quantization of the least quantum mechanical degrees of freedom.
Optimal combination of environmental cues and path integration during navigation.
Sjolund, Lori A; Kelly, Jonathan W; McNamara, Timothy P
2017-08-21
Navigation is influenced by body-based self-motion cues that are integrated over time, in a process known as path integration, as well as by environmental cues such as landmarks and room shape. In two experiments we explored whether humans combine path integration and environmental cues (Exp. 1: room shape; Exp. 2: room shape, single landmark, and multiple landmarks) to reduce response variability when returning to a previously visited location. Participants walked an outbound path in an immersive virtual environment before attempting to return to the path origin. Path integration and an environmental cue were both available during the outbound path, but experimental manipulations created single- and dual-cue conditions during the return path. The response variance when returning to the path origin was reduced when both cues were available, consistent with optimal integration predicted on the basis of Bayesian principles. The findings indicate that humans optimally integrate multiple spatial cues during navigation. Additionally, a large (but not a small) cue conflict caused participants to assign a higher weight to path integration than to environmental cues, despite the relatively greater precision afforded by the environmental cues.
Path-Integral Derivation of Lifshitz Tails
NASA Astrophysics Data System (ADS)
Sa-Yakanit, V.
2008-11-01
The behavior of the electron density of states (DOS) for the Lifshitz tail states is studied in the limit of low energy using the Feynman path-integral method. This method was used to study the heavily doped semiconductors for the case of a Gaussian random potential. The main results obtained are that the tail states behave as DOS exp (-B(E)), with B(E) = En, n = {1 / 2} for short-range interaction and n = 2 for long-range interaction. In this study it is shown that without the Gaussian approximation, the behavior of the Lifshitz tails for the Poisson distribution is obtained as DOS exp (-B(E)) with B(E) = En, n = {3 / 2} . As in the case of heavily doped semiconductor, the method can be easily generalized to long-range interactions. A comparison with the method developed by Friedberg and Luttinger based on the reformulation of the problem in terms of Brownian motion is given.
Differential neural network configuration during human path integration
Arnold, Aiden E. G. F; Burles, Ford; Bray, Signe; Levy, Richard M.; Iaria, Giuseppe
2014-01-01
Path integration is a fundamental skill for navigation in both humans and animals. Despite recent advances in unraveling the neural basis of path integration in animal models, relatively little is known about how path integration operates at a neural level in humans. Previous attempts to characterize the neural mechanisms used by humans to visually path integrate have suggested a central role of the hippocampus in allowing accurate performance, broadly resembling results from animal data. However, in recent years both the central role of the hippocampus and the perspective that animals and humans share similar neural mechanisms for path integration has come into question. The present study uses a data driven analysis to investigate the neural systems engaged during visual path integration in humans, allowing for an unbiased estimate of neural activity across the entire brain. Our results suggest that humans employ common task control, attention and spatial working memory systems across a frontoparietal network during path integration. However, individuals differed in how these systems are configured into functional networks. High performing individuals were found to more broadly express spatial working memory systems in prefrontal cortex, while low performing individuals engaged an allocentric memory system based primarily in the medial occipito-temporal region. These findings suggest that visual path integration in humans over short distances can operate through a spatial working memory system engaging primarily the prefrontal cortex and that the differential configuration of memory systems recruited by task control networks may help explain individual biases in spatial learning strategies. PMID:24808849
Differential neural network configuration during human path integration.
Arnold, Aiden E G F; Burles, Ford; Bray, Signe; Levy, Richard M; Iaria, Giuseppe
2014-01-01
Path integration is a fundamental skill for navigation in both humans and animals. Despite recent advances in unraveling the neural basis of path integration in animal models, relatively little is known about how path integration operates at a neural level in humans. Previous attempts to characterize the neural mechanisms used by humans to visually path integrate have suggested a central role of the hippocampus in allowing accurate performance, broadly resembling results from animal data. However, in recent years both the central role of the hippocampus and the perspective that animals and humans share similar neural mechanisms for path integration has come into question. The present study uses a data driven analysis to investigate the neural systems engaged during visual path integration in humans, allowing for an unbiased estimate of neural activity across the entire brain. Our results suggest that humans employ common task control, attention and spatial working memory systems across a frontoparietal network during path integration. However, individuals differed in how these systems are configured into functional networks. High performing individuals were found to more broadly express spatial working memory systems in prefrontal cortex, while low performing individuals engaged an allocentric memory system based primarily in the medial occipito-temporal region. These findings suggest that visual path integration in humans over short distances can operate through a spatial working memory system engaging primarily the prefrontal cortex and that the differential configuration of memory systems recruited by task control networks may help explain individual biases in spatial learning strategies.
Two-path plasmonic interferometer with integrated detector
Dyer, Gregory Conrad; Shaner, Eric A.; Aizin, Gregory
2016-03-29
An electrically tunable terahertz two-path plasmonic interferometer with an integrated detection element can down convert a terahertz field to a rectified DC signal. The integrated detector utilizes a resonant plasmonic homodyne mixing mechanism that measures the component of the plasma waves in-phase with an excitation field that functions as the local oscillator in the mixer. The plasmonic interferometer comprises two independently tuned electrical paths. The plasmonic interferometer enables a spectrometer-on-a-chip where the tuning of electrical path length plays an analogous role to that of physical path length in macroscopic Fourier transform interferometers.
Path integrals and the WKB approximation in loop quantum cosmology
NASA Astrophysics Data System (ADS)
Ashtekar, Abhay; Campiglia, Miguel; Henderson, Adam
2010-12-01
We follow the Feynman procedure to obtain a path integral formulation of loop quantum cosmology starting from the Hilbert space framework. Quantum geometry effects modify the weight associated with each path so that the effective measure on the space of paths is different from that used in the Wheeler-DeWitt theory. These differences introduce some conceptual subtleties in arriving at the WKB approximation. But the approximation is well defined and provides intuition for the differences between loop quantum cosmology and the Wheeler-DeWitt theory from a path integral perspective.
Selecta from a Life-Long Obsession with Path Integrals
Klauder, John R.
2008-06-18
The definition and interpretation of canonical, phase space path integrals has evolved over many years to achieve a form that now admits a correct and rigorous formulation, which is also covariant under canonical coordinate transformations. Such formulations involve coherent state representations, which, in their modern version, were originally introduced as an alternative tool to construct phase space path integrals. Moreover, coherent state representations lead to physical interpretations that are more natural than those afforded by more traditional representations. Suitable continuous time regularization procedures lead to a covariant phase space path integral formulation that greatly clarifies the vague phrase that canonical quantization requires Cartesian coordinates.
A Note on Feynman Path Integral for Electromagnetic External Fields
NASA Astrophysics Data System (ADS)
Botelho, Luiz C. L.
2017-08-01
We propose a Fresnel stochastic white noise framework to analyze the nature of the Feynman paths entering on the Feynman Path Integral expression for the Feynman Propagator of a particle quantum mechanically moving under an external electromagnetic time-independent potential.
The application of path integral for log return probability calculation
NASA Astrophysics Data System (ADS)
Palupi, D. S.; Hermanto, A.; Tenderlilin, E.; Rosyid, M. F.
2014-10-01
Log return probability has been calculated using path integral method. The stock price is assumed obeying the stochastic differential equation of a geometric Brownian motion and the volatility is assumed following Ornstein Uhlenbeck process. The stochastic differential equation of stock price and volatility lead to Fokker-Plank equation. The Fokker-Plank equation is solved using path integral method. Distribution of log return can be used to take the valuation ln return stock.
Variational path integral molecular dynamics study of a water molecule
NASA Astrophysics Data System (ADS)
Miura, Shinichi
2013-08-01
In the present study, a variational path integral molecular dynamics method developed by the author [Chem. Phys. Lett. 482, 165 (2009)] is applied to a water molecule on the adiabatic potential energy surface. The method numerically generates an exact wavefunction using a trial wavefunction of the target system. It has been shown that even if a poor trial wavefunction is employed, the exact quantum distribution is numerically extracted, demonstrating the robustness of the variational path integral method.
Sensory feedback in a bump attractor model of path integration.
Poll, Daniel B; Nguyen, Khanh; Kilpatrick, Zachary P
2016-04-01
Mammalian spatial navigation systems utilize several different sensory information channels. This information is converted into a neural code that represents the animal's current position in space by engaging place cell, grid cell, and head direction cell networks. In particular, sensory landmark (allothetic) cues can be utilized in concert with an animal's knowledge of its own velocity (idiothetic) cues to generate a more accurate representation of position than path integration provides on its own (Battaglia et al. The Journal of Neuroscience 24(19):4541-4550 (2004)). We develop a computational model that merges path integration with feedback from external sensory cues that provide a reliable representation of spatial position along an annular track. Starting with a continuous bump attractor model, we explore the impact of synaptic spatial asymmetry and heterogeneity, which disrupt the position code of the path integration process. We use asymptotic analysis to reduce the bump attractor model to a single scalar equation whose potential represents the impact of asymmetry and heterogeneity. Such imperfections cause errors to build up when the network performs path integration, but these errors can be corrected by an external control signal representing the effects of sensory cues. We demonstrate that there is an optimal strength and decay rate of the control signal when cues appear either periodically or randomly. A similar analysis is performed when errors in path integration arise from dynamic noise fluctuations. Again, there is an optimal strength and decay of discrete control that minimizes the path integration error.
Path Integrals and Exotic Options:. Methods and Numerical Results
NASA Astrophysics Data System (ADS)
Bormetti, G.; Montagna, G.; Moreni, N.; Nicrosini, O.
2005-09-01
In the framework of Black-Scholes-Merton model of financial derivatives, a path integral approach to option pricing is presented. A general formula to price path dependent options on multidimensional and correlated underlying assets is obtained and implemented by means of various flexible and efficient algorithms. As an example, we detail the case of Asian call options. The numerical results are compared with those obtained with other procedures used in quantitative finance and found to be in good agreement. In particular, when pricing at the money (ATM) and out of the money (OTM) options, path integral exhibits competitive performances.
Characterizing regulatory path motifs in integrated networks using perturbational data
2010-01-01
We introduce Pathicular http://bioinformatics.psb.ugent.be/software/details/Pathicular, a Cytoscape plugin for studying the cellular response to perturbations of transcription factors by integrating perturbational expression data with transcriptional, protein-protein and phosphorylation networks. Pathicular searches for 'regulatory path motifs', short paths in the integrated physical networks which occur significantly more often than expected between transcription factors and their targets in the perturbational data. A case study in Saccharomyces cerevisiae identifies eight regulatory path motifs and demonstrates their biological significance. PMID:20230615
A subterranean mammal uses the magnetic compass for path integration.
Kimchi, Tali; Etienne, Ariane S; Terkel, Joseph
2004-01-27
Path integration allows animals to navigate without landmarks by continuously processing signals generated through locomotion. Insects such as bees and ants have evolved an accurate path integration system, assessing and coding rotations with the help of a general directional reference, the sun azimuth. In mammals, by contrast, this process can take place through purely idiothetic (mainly proprioceptive and vestibular) signals. However, without any stable external reference for measuring direction, path integration is highly affected by cumulative errors and thus has been considered so far as valid only for short-distance navigation. Here we show through two path integration experiments (homing and shortcut finding) that the blind mole rat assesses direction both through internal signals and by estimating its heading in relation to the earth's magnetic field. Further, it is shown that the greater the circumvolution and length of the traveled path, the more the animal relies on the geomagnetic field. This path integration system strongly reduces the accumulation of errors due to inaccuracies in the estimation of rotations and thus allows the mole rat to navigate efficiently in darkness, without the help of any landmark, over both short and long distances.
The perturbative approach to path integrals: A succinct mathematical treatment
NASA Astrophysics Data System (ADS)
Nguyen, Timothy
2016-09-01
We study finite-dimensional integrals in a way that elucidates the mathematical meaning behind the formal manipulations of path integrals occurring in quantum field theory. This involves a proper understanding of how Wick's theorem allows one to evaluate integrals perturbatively, i.e., as a series expansion in a formal parameter irrespective of convergence properties. We establish invariance properties of such a Wick expansion under coordinate changes and the action of a Lie group of symmetries, and we use this to study essential features of path integral manipulations, including coordinate changes, Ward identities, Schwinger-Dyson equations, Faddeev-Popov gauge-fixing, and eliminating fields by their equation of motion. We also discuss the asymptotic nature of the Wick expansion and the implications this has for defining path integrals perturbatively and nonperturbatively.
Medial Temporal Lobe Roles in Human Path Integration
Yamamoto, Naohide; Philbeck, John W.; Woods, Adam J.; Gajewski, Daniel A.; Arthur, Joeanna C.; Potolicchio, Samuel J.; Levy, Lucien; Caputy, Anthony J.
2014-01-01
Path integration is a process in which observers derive their location by integrating self-motion signals along their locomotion trajectory. Although the medial temporal lobe (MTL) is thought to take part in path integration, the scope of its role for path integration remains unclear. To address this issue, we administered a variety of tasks involving path integration and other related processes to a group of neurosurgical patients whose MTL was unilaterally resected as therapy for epilepsy. These patients were unimpaired relative to neurologically intact controls in many tasks that required integration of various kinds of sensory self-motion information. However, the same patients (especially those who had lesions in the right hemisphere) walked farther than the controls when attempting to walk without vision to a previewed target. Importantly, this task was unique in our test battery in that it allowed participants to form a mental representation of the target location and anticipate their upcoming walking trajectory before they began moving. Thus, these results put forth a new idea that the role of MTL structures for human path integration may stem from their participation in predicting the consequences of one's locomotor actions. The strengths of this new theoretical viewpoint are discussed. PMID:24802000
Medial temporal lobe roles in human path integration.
Yamamoto, Naohide; Philbeck, John W; Woods, Adam J; Gajewski, Daniel A; Arthur, Joeanna C; Potolicchio, Samuel J; Levy, Lucien; Caputy, Anthony J
2014-01-01
Path integration is a process in which observers derive their location by integrating self-motion signals along their locomotion trajectory. Although the medial temporal lobe (MTL) is thought to take part in path integration, the scope of its role for path integration remains unclear. To address this issue, we administered a variety of tasks involving path integration and other related processes to a group of neurosurgical patients whose MTL was unilaterally resected as therapy for epilepsy. These patients were unimpaired relative to neurologically intact controls in many tasks that required integration of various kinds of sensory self-motion information. However, the same patients (especially those who had lesions in the right hemisphere) walked farther than the controls when attempting to walk without vision to a previewed target. Importantly, this task was unique in our test battery in that it allowed participants to form a mental representation of the target location and anticipate their upcoming walking trajectory before they began moving. Thus, these results put forth a new idea that the role of MTL structures for human path integration may stem from their participation in predicting the consequences of one's locomotor actions. The strengths of this new theoretical viewpoint are discussed.
Low level constraints on dynamic contour path integration.
Hall, Sophie; Bourke, Patrick; Guo, Kun
2014-01-01
Contour integration is a fundamental visual process. The constraints on integrating discrete contour elements and the associated neural mechanisms have typically been investigated using static contour paths. However, in our dynamic natural environment objects and scenes vary over space and time. With the aim of investigating the parameters affecting spatiotemporal contour path integration, we measured human contrast detection performance of a briefly presented foveal target embedded in dynamic collinear stimulus sequences (comprising five short 'predictor' bars appearing consecutively towards the fovea, followed by the 'target' bar) in four experiments. The data showed that participants' target detection performance was relatively unchanged when individual contour elements were separated by up to 2° spatial gap or 200 ms temporal gap. Randomising the luminance contrast or colour of the predictors, on the other hand, had similar detrimental effect on grouping dynamic contour path and subsequent target detection performance. Randomising the orientation of the predictors reduced target detection performance greater than introducing misalignment relative to the contour path. The results suggest that the visual system integrates dynamic path elements to bias target detection even when the continuity of path is disrupted in terms of spatial (2°), temporal (200 ms), colour (over 10 colours) and luminance (-25% to 25%) information. We discuss how the findings can be largely reconciled within the functioning of V1 horizontal connections.
Mielke, Steven L; Truhlar, Donald G
2016-01-21
Using Feynman path integrals, a molecular partition function can be written as a double integral with the inner integral involving all closed paths centered at a given molecular configuration, and the outer integral involving all possible molecular configurations. In previous work employing Monte Carlo methods to evaluate such partition functions, we presented schemes for importance sampling and stratification in the molecular configurations that constitute the path centroids, but we relied on free-particle paths for sampling the path integrals. At low temperatures, the path sampling is expensive because the paths can travel far from the centroid configuration. We now present a scheme for importance sampling of whole Feynman paths based on harmonic information from an instantaneous normal mode calculation at the centroid configuration, which we refer to as harmonically guided whole-path importance sampling (WPIS). We obtain paths conforming to our chosen importance function by rejection sampling from a distribution of free-particle paths. Sample calculations on CH4 demonstrate that at a temperature of 200 K, about 99.9% of the free-particle paths can be rejected without integration, and at 300 K, about 98% can be rejected. We also show that it is typically possible to reduce the overhead associated with the WPIS scheme by sampling the paths using a significantly lower-order path discretization than that which is needed to converge the partition function.
Canonical formulation and path integral for local vacuum energy sequestering
NASA Astrophysics Data System (ADS)
Bufalo, R.; KlusoÅ, J.; Oksanen, M.
2016-08-01
We establish the Hamiltonian analysis and the canonical path integral for a local formulation of vacuum energy sequestering. In particular, by considering the state of the Universe as a superposition of vacuum states corresponding to different values of the cosmological and gravitational constants, the path integral is extended to include integrations over the cosmological and gravitational constants. The result is an extension of the Ng-van Dam form of the path integral of unimodular gravity. It is argued to imply a relation between the fraction of the most likely values of the gravitational and cosmological constants and the average values of the energy density and pressure of matter over spacetime. Finally, we construct and analyze a Becchi-Rouet-Stora-Tyutin-exact formulation of the theory, which can be considered as a topological field theory.
Linearized path integral approach for calculating nonadiabatic time correlation functions.
Bonella, Sara; Montemayor, Daniel; Coker, David F
2005-05-10
We show that quantum time correlation functions including electronically nonadiabatic effects can be computed by using an approach in which their path integral expression is linearized in the difference between forward and backward nuclear paths while the electronic component of the amplitude, represented in the mapping formulation, can be computed exactly, leading to classical-like equations of motion for all degrees of freedom. The efficiency of this approach is demonstrated in some simple model applications.
Integrated Schools: Finding a New Path
ERIC Educational Resources Information Center
Orfield, Gary; Frankenberg, Erica; Siegel-Hawley, Genevieve
2010-01-01
Research shows that schools remain a powerful tool for shoring up individual opportunity and for attaining a thriving, multiracial democratic society. The authors point to social science evidence that demonstrates how segregated schooling limits the prospects of both minority and majority students and how integrated education can close the…
Path integral representation for polymer quantized scalar fields
NASA Astrophysics Data System (ADS)
Kajuri, Nirmalya
2015-12-01
According to loop quantum gravity, matter fields must be quantized in a background-independent manner. For scalar fields, such a background-independent quantization is called polymer quantization and is inequivalent to the standard Schrödinger quantization. It is therefore important to obtain predictions from the polymer quantized scalar field theory and compare with the standard results. As a step towards this, we develop a path integral representation for the polymer quantized scalar field. We notice several crucial differences from the path integral for the Schrödinger quantized scalar field. One important difference is the appearance of an extra summation at each point in the path integral for the polymer quantized theory. A second crucial difference is the loss of manifest Lorentz symmetry for a polymer quantized theory on Minkowski space.
Faddeev-Jackiw quantization and the path integral
NASA Astrophysics Data System (ADS)
Toms, David J.
2015-11-01
The method for quantization of constrained theories that was suggested originally by Faddeev and Jackiw along with later modifications is discussed. The particular emphasis of this paper is to show how it is simple to implement their method within the path integral framework using the natural geometric structure that their method utilizes. The procedure is exemplified with the analysis of two models: a quantum mechanical particle constrained to a surface (of which the hypersphere is a special case), and a quantized Schrödinger field interacting with a quantized vector field for both the massive and the massless cases. The results are shown to agree with what is found using the Dirac method for constrained path integrals. We comment on a previous path integral analysis of the Faddeev-Jackiw method. We also discuss why a previous criticism of the Faddeev-Jackiw method is unfounded and why suggested modifications of their method are unnecessary.
Master equations and the theory of stochastic path integrals.
Weber, Markus F; Frey, Erwin
2017-04-01
This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of master equations most often rely on low-noise approximations such as the Kramers-Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations. We focus on numerical and analytical methods going beyond the low-noise limit and provide a unified framework for the study of master equations. After deriving the forward and backward master equations from the Chapman-Kolmogorov equation, we show how the two master equations can be cast into either of four linear partial differential equations (PDEs). Three of these PDEs are discussed in detail. The first PDE governs the time evolution of a generalized probability generating function whose basis depends on the stochastic process under consideration. Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE. The second PDE is novel and is obeyed by a distribution that is marginalized over an initial state. It proves useful for the computation of mean extinction times. The third PDE describes the time evolution of a 'generating functional', which generalizes the so-called Poisson representation. Subsequently, the solutions of the PDEs are expressed in terms of two path integrals: a 'forward' and a 'backward' path integral. Combined with inverse transformations, one obtains two distinct path integral representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Moreover, we show how a well-known path integral representation of averaged observables can be recovered from them. Upon
Master equations and the theory of stochastic path integrals
NASA Astrophysics Data System (ADS)
Weber, Markus F.; Frey, Erwin
2017-04-01
This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of master equations most often rely on low-noise approximations such as the Kramers-Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations. We focus on numerical and analytical methods going beyond the low-noise limit and provide a unified framework for the study of master equations. After deriving the forward and backward master equations from the Chapman-Kolmogorov equation, we show how the two master equations can be cast into either of four linear partial differential equations (PDEs). Three of these PDEs are discussed in detail. The first PDE governs the time evolution of a generalized probability generating function whose basis depends on the stochastic process under consideration. Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE. The second PDE is novel and is obeyed by a distribution that is marginalized over an initial state. It proves useful for the computation of mean extinction times. The third PDE describes the time evolution of a ‘generating functional’, which generalizes the so-called Poisson representation. Subsequently, the solutions of the PDEs are expressed in terms of two path integrals: a ‘forward’ and a ‘backward’ path integral. Combined with inverse transformations, one obtains two distinct path integral representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Moreover, we show how a well-known path integral representation of averaged observables can be recovered from
Predator-prey quasicycles from a path-integral formalism.
Butler, Thomas; Reynolds, David
2009-03-01
The existence of beyond mean-field quasicycle oscillations in a simple spatial model of predator-prey interactions is derived from a path-integral formalism. The results agree substantially with those obtained from analysis of similar models using system size expansions of the master equation. In all of these analyses, the discrete nature of predator-prey populations and finite-size effects lead to persistent oscillations in time, but spatial patterns fail to form. The path-integral formalism goes beyond mean-field theory and provides a focus on individual realizations of the stochastic time evolution of population not captured in the standard master-equation approach.
Action with Acceleration i: Euclidean Hamiltonian and Path Integral
NASA Astrophysics Data System (ADS)
Baaquie, Belal E.
2013-10-01
An action having an acceleration term in addition to the usual velocity term is analyzed. The quantum mechanical system is directly defined for Euclidean time using the path integral. The Euclidean Hamiltonian is shown to yield the acceleration Lagrangian and the path integral with the correct boundary conditions. Due to the acceleration term, the state space depends on both position and velocity — and hence the Euclidean Hamiltonian depends on two degrees of freedom. The Hamiltonian for the acceleration system is non-Hermitian and can be mapped to a Hermitian Hamiltonian using a similarity transformation; the matrix elements of the similarity transformation are explicitly evaluated.
Linear Path Integration Deficits in Patients with Abnormal Vestibular Afference
Arthur, Joeanna C.; Kortte, Kathleen B.; Shelhamer, Mark; Schubert, Michael C.
2014-01-01
Effective navigation requires the ability to keep track of one’s location and maintain orientation during linear and angular displacements. Path integration is the process of updating the representation of body position by integrating internally-generated self-motion signals over time (e.g., walking in the dark). One major source of input to path integration is vestibular afference. We tested patients with reduced vestibular function (unilateral vestibular hypofunction, UVH), patients with aberrant vestibular function (benign paroxysmal positional vertigo, BPPV), and healthy participants (controls) on two linear path integration tasks: experimenter-guided walking and target-directed walking. The experimenter-guided walking task revealed a systematic underestimation of self-motion signals in UVH patients compared to the other groups. However, we did not find any difference in the distance walked between the UVH group and the control group for the target-directed walking task. Results from neuropsychological testing and clinical balance measures suggest that the errors in experimenter-guided walking were not attributable to cognitive and/or balance impairments. We conclude that impairment in linear path integration in UVH patients stem from deficits in self-motion perception. Importantly, our results also suggest that patients with a UVH deficit do not lose their ability to walk accurately without vision to a memorized target location. PMID:22726251
Path Integrals and the Statistical Thermodynamics of Black Holes.
NASA Astrophysics Data System (ADS)
Martinez, Erik Andres
The path integral is an important element in modern approaches to the quantization of the gravitational field. Path integral representations of partition functions for static and stationary black hole systems as well as path integrals for minisuperspace models of cosmology are presented. The functional integral is defined throughout as a sum over Lorentzian histories. A consistent formulation of Feynman's prescription to construct partition functions in terms of path integrals for general gravitational systems is presented and contrasted with other "Euclideanization" prescriptions. It is shown that the central object in the description of black hole systems is the gravitational action. In particular, the additivity of the entropies of matter and black holes in thermal equilibrium is a consequence of the additivity of their corresponding actions, and thermodynamic potentials like the energy or the pressure are not in general addivite when gravity plays an important role. Partition functions as stationary phase approximations of functional integrals for all the thermodynamic ensembles are then constructed by including gravitation as a part of the thermodynamical system. We show that a complex geometry is required to derive the thermodynamic properties of stationary geometries from the sum over histories. The corresponding real "thermodynamical" action is calculated explicitly and the thermodynamical data that imply thermal equilibrium in the presence of a rotating black hole in interaction with matter fields are presented and related to geometrical data. Some of the consequences for Kerr-Newman black hole systems are also discussed. For minisuperspace cosmologies the Lorentzian path integral is a Green function for the Wheeler-DeWitt operator, and its real part is a solution to the Wheeler -DeWitt equation. It is computed explicitly for the de Sitter minisuperspace model. The resulting Green function is then related to both the Hartle-Hawking and tunneling wave
Transport path optimization algorithm based on fuzzy integrated weights
NASA Astrophysics Data System (ADS)
Hou, Yuan-Da; Xu, Xiao-Hao
2014-11-01
Natural disasters cause significant damage to roads, making route selection a complicated logistical problem. To overcome this complexity, we present a method of using a trapezoidal fuzzy number to select the optimal transport path. Using the given trapezoidal fuzzy edge coefficients, we calculate a fuzzy integrated matrix, and incorporate the fuzzy multi-weights into fuzzy integrated weights. The optimal path is determined by taking two sets of vertices and transforming undiscovered vertices into discoverable ones. Our experimental results show that the model is highly accurate, and requires only a few measurement data to confirm the optimal path. The model provides an effective, feasible, and convenient method to obtain weights for different road sections, and can be applied to road planning in intelligent transportation systems.
The path integral formulation of climate dynamics.
Navarra, Antonio; Tribbia, Joe; Conti, Giovanni
2013-01-01
The chaotic nature of the atmospheric dynamics has stimulated the applications of methods and ideas derived from statistical dynamics. For instance, ensemble systems are used to make weather predictions recently extensive, which are designed to sample the phase space around the initial condition. Such an approach has been shown to improve substantially the usefulness of the forecasts since it allows forecasters to issue probabilistic forecasts. These works have modified the dominant paradigm of the interpretation of the evolution of atmospheric flows (and oceanic motions to some extent) attributing more importance to the probability distribution of the variables of interest rather than to a single representation. The ensemble experiments can be considered as crude attempts to estimate the evolution of the probability distribution of the climate variables, which turn out to be the only physical quantity relevant to practice. However, little work has been done on a direct modeling of the probability evolution itself. In this paper it is shown that it is possible to write the evolution of the probability distribution as a functional integral of the same kind introduced by Feynman in quantum mechanics, using some of the methods and results developed in statistical physics. The approach allows obtaining a formal solution to the Fokker-Planck equation corresponding to the Langevin-like equation of motion with noise. The method is very general and provides a framework generalizable to red noise, as well as to delaying differential equations, and even field equations, i.e., partial differential equations with noise, for example, general circulation models with noise. These concepts will be applied to an example taken from a simple ENSO model.
The Path Integral Formulation of Climate Dynamics
Navarra, Antonio; Tribbia, Joe; Conti, Giovanni
2013-01-01
The chaotic nature of the atmospheric dynamics has stimulated the applications of methods and ideas derived from statistical dynamics. For instance, ensemble systems are used to make weather predictions recently extensive, which are designed to sample the phase space around the initial condition. Such an approach has been shown to improve substantially the usefulness of the forecasts since it allows forecasters to issue probabilistic forecasts. These works have modified the dominant paradigm of the interpretation of the evolution of atmospheric flows (and oceanic motions to some extent) attributing more importance to the probability distribution of the variables of interest rather than to a single representation. The ensemble experiments can be considered as crude attempts to estimate the evolution of the probability distribution of the climate variables, which turn out to be the only physical quantity relevant to practice. However, little work has been done on a direct modeling of the probability evolution itself. In this paper it is shown that it is possible to write the evolution of the probability distribution as a functional integral of the same kind introduced by Feynman in quantum mechanics, using some of the methods and results developed in statistical physics. The approach allows obtaining a formal solution to the Fokker-Planck equation corresponding to the Langevin-like equation of motion with noise. The method is very general and provides a framework generalizable to red noise, as well as to delaying differential equations, and even field equations, i.e., partial differential equations with noise, for example, general circulation models with noise. These concepts will be applied to an example taken from a simple ENSO model. PMID:23840577
Path Integral for Dirac oscillator with generalized uncertainty principle
Benzair, H.; Boudjedaa, T.; Merad, M.
2012-12-15
The propagator for Dirac oscillator in (1+1) dimension, with deformed commutation relation of the Heisenberg principle, is calculated using path integral in quadri-momentum representation. As the mass is related to momentum, we then adapt the space-time transformation method to evaluate quantum corrections and this latter is dependent from the point discretization interval.
Piloting Systems Reset Path Integration Systems during Position Estimation
ERIC Educational Resources Information Center
Zhang, Lei; Mou, Weimin
2017-01-01
During locomotion, individuals can determine their positions with either idiothetic cues from movement (path integration systems) or visual landmarks (piloting systems). This project investigated how these 2 systems interact in determining humans' positions. In 2 experiments, participants studied the locations of 5 target objects and 1 single…
The functional measure for the in-in path integral
NASA Astrophysics Data System (ADS)
Kaya, Ali
2015-05-01
The in-in path integral of a scalar field propagating in a fixed background is formulated in a suitable function space. The free kinetic operator, whose inverse gives the propagators of the in-in perturbation theory, becomes essentially self adjoint after imposing appropriate boundary conditions. An explicit spectral representation is given for the scalar in the flat space, and the standard propagators are rederived using this representation. In this way the subtle boundary path integral over the field configurations at the return time is handled straightforwardly. It turns out that not only the values of the forward (+) and the backward (-) evolving fields but also their time derivatives must be matched at the return time, which is mainly overlooked in the literature. This formulation also determines the field configurations that are included in the path integral uniquely. We show that some of the recently suggested instanton-like solutions corresponding to the stationary phases of the cosmological in-in path integrals can be rigorously identified as limits of sequences in the function space.
Quantum tunneling splittings from path-integral molecular dynamics
NASA Astrophysics Data System (ADS)
Mátyus, Edit; Wales, David J.; Althorpe, Stuart C.
2016-03-01
We illustrate how path-integral molecular dynamics can be used to calculate ground-state tunnelling splittings in molecules or clusters. The method obtains the splittings from ratios of density matrix elements between the degenerate wells connected by the tunnelling. We propose a simple thermodynamic integration scheme for evaluating these elements. Numerical tests on fully dimensional malonaldehyde yield tunnelling splittings in good overall agreement with the results of diffusion Monte Carlo calculations.
What is the right time for path integrals?
NASA Astrophysics Data System (ADS)
Jones, Eric; Bach, Roger; Batelaan, Herman
2013-05-01
The Feynman path integral formulation of quantum mechanics has proven to be a powerful tool for calculations in matter optics. It is natural to introduce the path integral in the context of Young's double slit experiment for matter waves as Feynman did, perhaps after discussing the analogous situation for optics. While intuitive, this approach can lead to a pedagogical misrepresentation of the theory, namely in the phase accumulated along single free-particle trajectories. How is the use of the accumulated phase, 2 πL /λdB , along a path of length L justified? The free-particle action gives a phase that differs by a factor of two. The guiding principle that interference occurs only for two paths that are indistinguishable from one another provides a correct solution: interfering paths must originate and terminate at equal times. We will present several simple thought experiments to illustrate incorrect and correct methods for determining phase shifts. We gratefully acknowledge support from NSF and the DoE GAANN. We thank Ron Cappelletti for interesting discussions.
Path integrals and large deviations in stochastic hybrid systems
NASA Astrophysics Data System (ADS)
Bressloff, Paul C.; Newby, Jay M.
2014-04-01
We construct a path-integral representation of solutions to a stochastic hybrid system, consisting of one or more continuous variables evolving according to a piecewise-deterministic dynamics. The differential equations for the continuous variables are coupled to a set of discrete variables that satisfy a continuous-time Markov process, which means that the differential equations are only valid between jumps in the discrete variables. Examples of stochastic hybrid systems arise in biophysical models of stochastic ion channels, motor-driven intracellular transport, gene networks, and stochastic neural networks. We use the path-integral representation to derive a large deviation action principle for a stochastic hybrid system. Minimizing the associated action functional with respect to the set of all trajectories emanating from a metastable state (assuming that such a minimization scheme exists) then determines the most probable paths of escape. Moreover, evaluating the action functional along a most probable path generates the so-called quasipotential used in the calculation of mean first passage times. We illustrate the theory by considering the optimal paths of escape from a metastable state in a bistable neural network.
Integration across Time Determines Path Deviation Discrimination for Moving Objects.
Whitaker, David; Levi, Dennis M; Kennedy, Graeme J
2008-04-16
Human vision is vital in determining our interaction with the outside world. In this study we characterize our ability to judge changes in the direction of motion of objects-a common task which can allow us either to intercept moving objects, or else avoid them if they pose a threat. Observers were presented with objects which moved across a computer monitor on a linear path until the midline, at which point they changed their direction of motion, and observers were required to judge the direction of change. In keeping with the variety of objects we encounter in the real world, we varied characteristics of the moving stimuli such as velocity, extent of motion path and the object size. Furthermore, we compared performance for moving objects with the ability of observers to detect a deviation in a line which formed the static trace of the motion path, since it has been suggested that a form of static memory trace may form the basis for these types of judgment. The static line judgments were well described by a 'scale invariant' model in which any two stimuli which possess the same two-dimensional geometry (length/width) result in the same level of performance. Performance for the moving objects was entirely different. Irrespective of the path length, object size or velocity of motion, path deviation thresholds depended simply upon the duration of the motion path in seconds. Human vision has long been known to integrate information across space in order to solve spatial tasks such as judgment of orientation or position. Here we demonstrate an intriguing mechanism which integrates direction information across time in order to optimize the judgment of path deviation for moving objects.
Free energies from integral equation theories: enforcing path independence.
Kast, Stefan M
2003-04-01
A variational formalism is constructed for deriving the chemical potential and the Helmholtz free energy in various statistical-mechanical integral equation theories of fluids. Nonzero bridge functions extending the scope of the theories beyond the hypernetted chain approximation can be classified as to whether or not they imply path dependence of the free energy. Classes of bridge functions free of the path dependence problem are derived, based on which a route is devised toward direct computation of free energies from the simulation of a single state.
Tackling higher derivative ghosts with the Euclidean path integral
Fontanini, Michele; Trodden, Mark
2011-05-15
An alternative to the effective field theory approach to treat ghosts in higher derivative theories is to attempt to integrate them out via the Euclidean path integral formalism. It has been suggested that this method could provide a consistent framework within which we might tolerate the ghost degrees of freedom that plague, among other theories, the higher derivative gravity models that have been proposed to explain cosmic acceleration. We consider the extension of this idea to treating a class of terms with order six derivatives, and find that for a general term the Euclidean path integral approach works in the most trivial background, Minkowski. Moreover we see that even in de Sitter background, despite some difficulties, it is possible to define a probability distribution for tensorial perturbations of the metric.
NASA Astrophysics Data System (ADS)
Kleinert, H.; Chervyakov, A.
2000-03-01
We show how to perform integrals over products of distributions in coordinate space such as to reproduce the results of momentum space Feynman integrals in dimensional regularization. This ensures the invariance of path integrals under coordinate transformations. The integrals are performed by expressing the propagators in /1-ɛ dimensions in terms of modified Bessel functions.
Beam spread functions calculated using Feynman path integrals
NASA Astrophysics Data System (ADS)
Kilgo, Paul; Tessendorf, Jerry
2017-07-01
A method of solving the radiative transfer equation using Feynman path integrals (FPIs) is discussed. The FPI approach is a mathematical framework for computing multiple scattering in participating media. Its numerical behavior is not well known, and techniques are being developed to solve the FPI approach numerically. A missing numerical technique is detailed and used to calculate beam spread functions (BSFs), a commonly studied experimental property of many types of media. The calculations are compared against measured BSFs of sea ice. Analysis shows differently-shaped BSFs, and suggests the width parameter of the calculated BSF's Gaussian fit approaches a value in the limit of the number of path segments. A projection is attempted, but suggests a larger number of path segments would not increase the width of the calculated BSF. The trial suggests the approach is numerically stable, but requires further testing to ensure scientific accuracy.
BOOK REVIEW: Path Integrals in Field Theory: An Introduction
NASA Astrophysics Data System (ADS)
Ryder, Lewis
2004-06-01
In the 1960s Feynman was known to particle physicists as one of the people who solved the major problems of quantum electrodynamics, his contribution famously introducing what are now called Feynman diagrams. To other physicists he gained a reputation as the author of the Feynman Lectures on Physics; in addition some people were aware of his work on the path integral formulation of quantum theory, and a very few knew about his work on gravitation and Yang--Mills theories, which made use of path integral methods. Forty years later the scene is rather different. Many of the problems of high energy physics are solved; and the standard model incorporates Feynman's path integral method as a way of proving the renormalisability of the gauge (Yang--Mills) theories involved. Gravitation is proving a much harder nut to crack, but here also questions of renormalisability are couched in path-integral language. What is more, theoretical studies of condensed matter physics now also appeal to this technique for quantisation, so the path integral method is becoming part of the standard apparatus of theoretical physics. Chapters on it appear in a number of recent books, and a few books have appeared devoted to this topic alone; the book under review is a very recent one. Path integral techniques have the advantage of enormous conceptual appeal and the great disadvantage of mathematical complexity, this being partly the result of messy integrals but more fundamentally due to the notions of functional differentiation and integration which are involved in the method. All in all this subject is not such an easy ride. Mosel's book, described as an introduction, is aimed at graduate students and research workers in particle physics. It assumes a background knowledge of quantum mechanics, both non-relativistic and relativistic. After three chapters on the path integral formulation of non-relativistic quantum mechanics there are eight chapters on scalar and spinor field theory, followed
Path integration and perturbation theory with complex Euclidean actions
Alexanian, Garnik; MacKenzie, R.; Paranjape, M. B.; Ruel, Jonathan
2008-05-15
The Euclidean path integral quite often involves an action that is not completely real, i.e. a complex action. This occurs when the Minkowski action contains t-odd CP-violating terms. This usually consists of topological terms, such as the Chern-Simons term in odd dimensions, the Wess-Zumino term, the {theta} term or Chern character in 4-dimensional gauge theories, or other topological densities. Analytic continuation to Euclidean time yields an imaginary term in the Euclidean action. It also occurs when the action contains fermions, the fermion path integral being in general a sum over positive and negative real numbers. Negative numbers correspond to the exponential of i{pi} and hence indicate the presence of an imaginary term in the action. In the presence of imaginary terms in the Euclidean action, the usual method of perturbative quantization can fail. Here the action is expanded about its critical points, the quadratic part serving to define the Gaussian free theory and the higher order terms defining the perturbative interactions. For a complex action, the critical points are generically obtained at complex field configurations. Hence the contour of path integration does not pass through the critical points and the perturbative paradigm cannot be directly implemented. The contour of path integration has to be deformed to pass through the complex critical point using a generalized method of steepest descent, in order to do so. Typically, this procedure is not followed. Rather, only the real part of the Euclidean action is considered, and its critical points are used to define the perturbation theory, a procedure that can lead to incorrect results. In this article we present a simple example to illustrate this point. The example consists of N scalar fields in 0+1 dimensions interacting with a U(1) gauge field in the presence of a Chern-Simons term. In this example the path integral can be done exactly, the procedure of deformation of the contour of path
Three dimensional path integration in the house mouse (Mus domestica).
Bardunias, P M; Jander, R
2000-12-01
Previous studies have explored two-dimensional path integration in rodents by recording responses to passive rotation on a horizontal plane. This study adds the element of passive rotation in a vertical plane, necessitating the mouse to integrate positional information from three dimensions. Mice were trained to climb a wire mesh joining two horizontal planes. The whole arena was rotated 90 degrees while the mouse was vertically oriented as it moved between planes. Rotation was conducted both clockwise and counter-clockwise, controls being provided by rotation of the arena while the mouse was in its nest-box. All 16 mice tested altered their direction of travel subsequent to rotation in the vertical plane, compensating with a change in their path on the following horizontal plane.
A path integral approach to age dependent branching processes
NASA Astrophysics Data System (ADS)
Greenman, Chris D.
2017-03-01
Age dependent population dynamics are frequently modeled with generalizations of the classic McKendrick–von Foerster equation. These are deterministic systems, and a stochastic generalization was recently reported in Greenman and Chou (2016 Phys. Rev. E 93 012112, 2016 J. Stat. Phys. 16449). Here we develop a fully stochastic theory for age-structured populations via quantum field theoretical Doi–Peliti techniques. This results in a path integral formulation where birth and death events correspond to cubic and quadratic interaction terms. This formalism allows us to efficiently recapitulate the results in Greenman and Chou (2016 Phys. Rev. E 93 012112, 2016 J. Stat. Phys. 16449), exemplifying the utility of Doi–Peliti methods. Furthermore, we find that the path integral formulation for age-structured moments has an exact perturbative expansion that explicitly relates to the hereditary structure between correlated individuals. These methods are then generalized with a binary fission model of cell division.
Three dimensional path integration in the house mouse (Mus domestica)
NASA Astrophysics Data System (ADS)
Bardunias, Paul M.; Jander, R.
Previous studies have explored two-dimensional path integration in rodents by recording responses to passive rotation on a horizontal plane. This study adds the element of passive rotation in a vertical plane, necessitating the mouse to integrate positional information from three dimensions. Mice were trained to climb a wire mesh joining two horizontal planes. The whole arena was rotated 90° while the mouse was vertically oriented as it moved between planes. Rotation was conducted both clockwise and counter-clockwise, controls being provided by rotation of the arena while the mouse was in its nest-box. All 16 mice tested altered their direction of travel subsequent to rotation in the vertical plane, compensating with a change in their path on the following horizontal plane.
On the Path Integral in Non-Commutative (nc) Qft
NASA Astrophysics Data System (ADS)
Dehne, Christoph
2008-09-01
As is generally known, different quantization schemes applied to field theory on NC spacetime lead to Feynman rules with different physical properties, if time does not commute with space. In particular, the Feynman rules that are derived from the path integral corresponding to the T*-product (the so-called naïve Feynman rules) violate the causal time ordering property. Within the Hamiltonian approach to quantum field theory, we show that we can (formally) modify the time ordering encoded in the above path integral. The resulting Feynman rules are identical to those obtained in the canonical approach via the Gell-Mann-Low formula (with T-ordering). They preserve thus unitarity and causal time ordering.
Path integral Liouville dynamics for thermal equilibrium systems.
Liu, Jian
2014-06-14
We show a new imaginary time path integral based method--path integral Liouville dynamics (PILD), which can be derived from the equilibrium Liouville dynamics [J. Liu and W. H. Miller, J. Chem. Phys. 134, 104101 (2011)] in the Wigner phase space. Numerical tests of PILD with the simple (white noise) Langevin thermostat have been made for two strongly anharmonic model problems. Since implementation of PILD does not request any specific form of the potential energy surface, the results suggest that PILD offers a potentially useful approach for general condensed phase molecular systems to have the two important properties: conserves the quantum canonical distribution and recovers exact thermal correlation functions (of even nonlinear operators, i.e., nonlinear functions of position or momentum operators) in the classical, high temperature, and harmonic limits.
Path integral Liouville dynamics for thermal equilibrium systems
Liu, Jian
2014-06-14
We show a new imaginary time path integral based method—path integral Liouville dynamics (PILD), which can be derived from the equilibrium Liouville dynamics [J. Liu and W. H. Miller, J. Chem. Phys. 134, 104101 (2011)] in the Wigner phase space. Numerical tests of PILD with the simple (white noise) Langevin thermostat have been made for two strongly anharmonic model problems. Since implementation of PILD does not request any specific form of the potential energy surface, the results suggest that PILD offers a potentially useful approach for general condensed phase molecular systems to have the two important properties: conserves the quantum canonical distribution and recovers exact thermal correlation functions (of even nonlinear operators, i.e., nonlinear functions of position or momentum operators) in the classical, high temperature, and harmonic limits.
Path integral for the relativistic particle in curved space
NASA Astrophysics Data System (ADS)
Ferraro, Rafael
1992-02-01
The propagator for a single relativistic particle in a (D+1)-dimensional curved background is obtained by evaluating the canonical path integral in the true 2D-dimensional phase space. Since only paths moving forward in time are integrated, the resulting propagator depends on how the time is chosen; i.e., it depends on the reference system. In order for the propagator to satisfy the properties of a unitary theory, the time must be attached to a Killing vector. Although the measure is unique (it is the Liouville measure), the skeletonization of the phase-space functional action is ambiguous. One such ambiguity is exploited to obtain different propagators obeying the Klein-Gordon equation with different couplings to quantities related to the shape of the reference system (spatial curvature, etc.).
Spin foam models for quantum gravity from lattice path integrals
Bonzom, Valentin
2009-09-15
Spin foam models for quantum gravity are derived from lattice path integrals. The setting involves variables from both lattice BF theory and Regge calculus. The action consists in a Regge action, which depends on areas, dihedral angles and includes the Immirzi parameter. In addition, a measure is inserted to ensure a consistent gluing of simplices, so that the amplitude is dominated by configurations that satisfy the parallel transport relations. We explicitly compute the path integral as a sum over spin foams for a generic measure. The Freidel-Krasnov and Engle-Pereira-Rovelli models correspond to a special choice of gluing. In this case, the equations of motion describe genuine geometries, where the constraints of area-angle Regge calculus are satisfied. Furthermore, the Immirzi parameter drops out of the on-shell action, and stationarity with respect to area variations requires spacetime geometry to be flat.
Asymptotics of Selberg-like integrals by lattice path counting
Novaes, Marcel
2011-04-15
We obtain explicit expressions for positive integer moments of the probability density of eigenvalues of the Jacobi and Laguerre random matrix ensembles, in the asymptotic regime of large dimension. These densities are closely related to the Selberg and Selberg-like multidimensional integrals. Our method of solution is combinatorial: it consists in the enumeration of certain classes of lattice paths associated to the solution of recurrence relations.
A path to integration in an academic health science center.
Panko, W B; Wilson, W
1992-01-01
This article describes a networking and integration strategy in use at the University of Michigan Medical Center. This strategy builds upon the existing technology base and is designed to provide a roadmap that will direct short-term development along a productive, long-term path. It offers a way to permit the short-term development of incremental solutions to current problems while at the same time maximizing the likelihood that these incremental efforts can be recycled into a more comprehensive approach.
Path integral analysis of Jarzynski's equality: analytical results.
Minh, David D L; Adib, Artur B
2009-02-01
We apply path integrals to study nonequilibrium work theorems in the context of Brownian dynamics, deriving in particular the equations of motion governing the most typical and most dominant trajectories. For the analytically soluble cases of a moving harmonic potential and a harmonic oscillator with a time-dependent natural frequency, we find such trajectories, evaluate the work-weighted propagators, and validate Jarzynski's equality.
Integration of Hierarchical Goal Network Planning and Autonomous Path Planning
2016-03-01
world robotic systems. This report documents work to integrate a hierarchical goal network planning algorithm with low-level path planning. The system...goals state. The domain is a robot operating in a known office environment with labeled rooms and doors that can be manipulated. The report goes on to...discuss future improvement of the system with the goal of creating a robust system that can operate on a robotic platform in a dynamic environment
Path integral approach to the quantum fidelity amplitude
2016-01-01
The Loschmidt echo is a measure of quantum irreversibility and is determined by the fidelity amplitude of an imperfect time-reversal protocol. Fidelity amplitude plays an important role both in the foundations of quantum mechanics and in its applications, such as time-resolved electronic spectroscopy. We derive an exact path integral formula for the fidelity amplitude and use it to obtain a series of increasingly accurate semiclassical approximations by truncating an exact expansion of the path integral exponent. While the zeroth-order expansion results in a remarkably simple, yet non-trivial approximation for the fidelity amplitude, the first-order expansion yields an alternative derivation of the so-called ‘dephasing representation,’ circumventing the use of a semiclassical propagator as in the original derivation. We also obtain an approximate expression for fidelity based on the second-order expansion, which resolves several shortcomings of the dephasing representation. The rigorous derivation from the path integral permits the identification of sufficient conditions under which various approximations obtained become exact. PMID:27140973
Efficient stochastic thermostatting of path integral molecular dynamics
NASA Astrophysics Data System (ADS)
Ceriotti, Michele; Parrinello, Michele; Markland, Thomas E.; Manolopoulos, David E.
2010-09-01
The path integral molecular dynamics (PIMD) method provides a convenient way to compute the quantum mechanical structural and thermodynamic properties of condensed phase systems at the expense of introducing an additional set of high frequency normal modes on top of the physical vibrations of the system. Efficiently sampling such a wide range of frequencies provides a considerable thermostatting challenge. Here we introduce a simple stochastic path integral Langevin equation (PILE) thermostat which exploits an analytic knowledge of the free path integral normal mode frequencies. We also apply a recently developed colored noise thermostat based on a generalized Langevin equation (GLE), which automatically achieves a similar, frequency-optimized sampling. The sampling efficiencies of these thermostats are compared with that of the more conventional Nosé-Hoover chain (NHC) thermostat for a number of physically relevant properties of the liquid water and hydrogen-in-palladium systems. In nearly every case, the new PILE thermostat is found to perform just as well as the NHC thermostat while allowing for a computationally more efficient implementation. The GLE thermostat also proves to be very robust delivering a near-optimum sampling efficiency in all of the cases considered. We suspect that these simple stochastic thermostats will therefore find useful application in many future PIMD simulations.
Path integral approach to the quantum fidelity amplitude.
Vaníček, Jiří; Cohen, Doron
2016-06-13
The Loschmidt echo is a measure of quantum irreversibility and is determined by the fidelity amplitude of an imperfect time-reversal protocol. Fidelity amplitude plays an important role both in the foundations of quantum mechanics and in its applications, such as time-resolved electronic spectroscopy. We derive an exact path integral formula for the fidelity amplitude and use it to obtain a series of increasingly accurate semiclassical approximations by truncating an exact expansion of the path integral exponent. While the zeroth-order expansion results in a remarkably simple, yet non-trivial approximation for the fidelity amplitude, the first-order expansion yields an alternative derivation of the so-called 'dephasing representation,' circumventing the use of a semiclassical propagator as in the original derivation. We also obtain an approximate expression for fidelity based on the second-order expansion, which resolves several shortcomings of the dephasing representation. The rigorous derivation from the path integral permits the identification of sufficient conditions under which various approximations obtained become exact.
Electronic Stroke CarePath: Integrated Approach to Stroke Care.
Katzan, Irene L; Fan, Youran; Speck, Micheal; Morton, Johanna; Fromwiller, Lauren; Urchek, John; Uchino, Ken; Griffith, Sandra D; Modic, Michael
2015-10-01
We describe the development, implementation, and outcomes of the first 2 years of the Electronic Stroke CarePath, an initiative developed for management of ischemic stroke patients in an effort to improve efficiency and quality of care for patients. The CarePath consists of care pathways for ischemic stroke that are integrated within the electronic health record. Patient-reported outcomes are collected using an external software platform. Documentation tools, order sets, and clinical decision support were designed to improve efficiency, optimize process measure adherence, and produce clinical data as a byproduct of care that are available for future analyses. Inpatient mortality and length of stay were compared before and after CarePath implementation in ischemic stroke patients after adjustment for case-mix. Postdischarge functional outcomes of patients with ischemic stroke were compared between the first 3 months of rollout and remainder of the study period. From January 2011 to December 2012, there were 1106 patients with ischemic stroke on the CarePath. There was a decline in inpatient mortality in patients with ischemic stroke, but not in control patients with intracerebral or subarachnoid hemorrhage. Completion rate of patient-reported questionnaires at postdischarge stroke follow-up was 72.9%. There was a trend toward improved functional outcomes at follow-up with CarePath implementation. Implementation of the Electronic Stroke CarePath is feasible and may be associated with a benefit in multiple different outcomes after ischemic stroke. This approach may be an important strategy for optimizing stroke care in the future.
Federal Register 2010, 2011, 2012, 2013, 2014
2012-12-12
... From the Federal Register Online via the Government Publishing Office INTERNATIONAL TRADE COMMISSION Certain Integrated Circuit Packages Provided with Multiple Heat- Conducting Paths and Products... integrated circuit packages provided with multiple heat-conducting paths and products containing same...
Stringer, Simon M; Rolls, Edmund T
2006-12-01
A key issue is how networks in the brain learn to perform path integration, that is update a represented position using a velocity signal. Using head direction cells as an example, we show that a competitive network could self-organize to learn to respond to combinations of head direction and angular head rotation velocity. These combination cells can then be used to drive a continuous attractor network to the next head direction based on the incoming rotation signal. An associative synaptic modification rule with a short term memory trace enables preceding combination cell activity during training to be associated with the next position in the continuous attractor network. The network accounts for the presence of neurons found in the brain that respond to combinations of head direction and angular head rotation velocity. Analogous networks in the hippocampal system could self-organize to perform path integration of place and spatial view representations.
From conformal blocks to path integrals in the Vaidya geometry
NASA Astrophysics Data System (ADS)
Anous, Tarek; Hartman, Thomas; Rovai, Antonin; Sonner, Julian
2017-09-01
Correlators in conformal field theory are naturally organized as a sum over conformal blocks. In holographic theories, this sum must reorganize into a path integral over bulk fields and geometries. We explore how these two sums are related in the case of a point particle moving in the background of a 3d collapsing black hole. The conformal block expansion is recast as a sum over paths of the first-quantized particle moving in the bulk geometry. Off-shell worldlines of the particle correspond to subdominant contributions in the Euclidean conformal block expansion, but these same operators must be included in order to correctly reproduce complex saddles in the Lorentzian theory. During thermalization, a complex saddle dominates under certain circumstances; in this case, the CFT correlator is not given by the Virasoro identity block in any channel, but can be recovered by summing heavy operators. This effectively converts the conformal block expansion in CFT from a sum over intermediate states to a sum over channels that mimics the bulk path integral.
Path integral based calculations of symmetrized time correlation functions. II.
Bonella, S; Monteferrante, M; Pierleoni, C; Ciccotti, G
2010-10-28
Schofield's form of quantum time correlation functions is used as the starting point to derive a computable expression for these quantities. The time composition property of the propagators in complex time is exploited to approximate Schofield's function in terms of a sequence of short time classical propagations interspersed with path integrals that, combined, represent the thermal density of the system. The approximation amounts to linearization of the real time propagators and it becomes exact with increasing number of propagation legs. Within this scheme, the correlation function is interpreted as an expectation value over a probability density defined on the thermal and real path space and calculated by a Monte Carlo algorithm. The performance of the algorithm is tested on a set of benchmark problems. Although the numerical effort required is considerable, we show that the algorithm converges systematically to the exact answer with increasing number of iterations and that it is stable for times longer than those accessible via a brute force, path integral based, calculation of the correlation function. Scaling of the algorithm with dimensionality is also examined and, when the method is combined with commonly used filtering schemes, found to be comparable to that of alternative semiclassical methods.
Path integral molecular dynamics at zero thermal temperature
NASA Astrophysics Data System (ADS)
Willow, Soohaeng Yoo
2017-04-01
Path integral molecular dynamics (PIMD) simulations at the zero thermal temperature still remain inconceivable. Herein, the quantum-mechanical partition function is revised in conjunction with the time-independent Schrödinger equation. The imaginary temperature for the quantum-mechanical partition function is introduced as an independent variable and defined under the guidance of the virial theorem. In the end, computational evidences are provided showing that this revised PIMD simulation at the zero thermal temperature reproduces both the zero-point energy and the probability density obtained from the Schrödinger equation for the harmonic oscillator.
Quantum corrections from a path integral over reparametrizations
Makeenko, Yuri; Olesen, Poul
2010-08-15
We study the path integral over reparametrizations that has been proposed as an ansatz for the Wilson loops in the large-N QCD and reproduces the area law in the classical limit of large loops. We show that a semiclassical expansion for a rectangular loop captures the Luescher term associated with d=26 dimensions and propose a modification of the ansatz that reproduces the Luescher term in other dimensions, which is observed in lattice QCD. We repeat the calculation for an outstretched ellipse advocating the emergence of an analog of the Luescher term and verify this result by a direct computation of the determinant of the Laplace operator and the conformal anomaly.
Path-integral formula for local thermal equilibrium
NASA Astrophysics Data System (ADS)
Hongo, Masaru
2017-08-01
We develop a complete path-integral formulation of relativistic quantum fields in local thermal equilibrium, which brings about the emergence of thermally induced curved spacetime. The resulting action is shown to have full diffeomorphism invariance and gauge invariance in thermal spacetime with imaginary-time independent backgrounds. This leads to the notable symmetry properties of emergent thermal spacetime: Kaluza-Klein gauge symmetry, spatial diffeomorphism symmetry, and gauge symmetry. A thermodynamic potential in local thermal equilibrium, or the so-called Massieu-Planck functional, is identified as a generating functional for conserved currents such as the energy-momentum tensor and the electric current.
Path-integral approach to the Wigner-Kirkwood expansion.
Jizba, Petr; Zatloukal, Václav
2014-01-01
We study the high-temperature behavior of quantum-mechanical path integrals. Starting from the Feynman-Kac formula, we derive a functional representation of the Wigner-Kirkwood perturbation expansion for quantum Boltzmann densities. As shown by its applications to different potentials, the presented expansion turns out to be quite efficient in generating analytic form of the higher-order expansion coefficients. To put some flesh on the bare bones, we apply the expansion to obtain basic thermodynamic functions of the one-dimensional anharmonic oscillator. Further salient issues, such as generalization to the Bloch density matrix and comparison with the more customary world-line formulation, are discussed.
A path to integration in an academic health science center.
Panko, W. B.; Wilson, W.
1992-01-01
This article describes a networking and integration strategy in use at the University of Michigan Medical Center. This strategy builds upon the existing technology base and is designed to provide a roadmap that will direct short-term development along a productive, long-term path. It offers a way to permit the short-term development of incremental solutions to current problems while at the same time maximizing the likelihood that these incremental efforts can be recycled into a more comprehensive approach. PMID:1336413
Exact path integral treatment of a diatomic molecule potential
Benamira, F.; Guechi, L.; Mameri, S.; Sadoun, M. A.
2007-03-15
A rigorous evaluation of the path integral for Green's function associated with a four-parameter potential for a diatomic molecule is presented. A closed form of Green's function is obtained for different shapes of this potential. When the deformation parameter {lambda} is {lambda}<0 or 0<{lambda}<1, it is found that the quantization conditions are transcendental equations that require a numerical solution. For {lambda}{>=}1 and r set-membership sign](1/{eta})ln {lambda},{infinity}[, the energy spectrum and the normalized wave functions of the bound states are derived. Particular cases of this potential which appear in the literature are also briefly discussed.
Remarks on the Origin of Path Integration:. Einstein and Feynman
NASA Astrophysics Data System (ADS)
Sauer, T.
2008-11-01
I offer some historical comments about the origins of Feynman's path-integral approach, as an alternative approach to standard quantum mechanics. Looking at the interaction between Einstein and Feynman, which was mediated by Feynman's thesis supervisor John Wheeler, it is argued that, contrary to what one might expect, the significance of the interaction between Einstein and Feynman pertained to a critique of classical field theory, rather than to a direct critique of quantum mechanics itself. Nevertheless, the critical perspective on classical field theory became a motivation and point of departure for Feynman's space-time approach to non-relativistic quantum mechanics.
Idiothetic Path Integration in the Fruit Fly Drosophila melanogaster.
Kim, Irene S; Dickinson, Michael H
2017-08-07
After discovering a small drop of food, hungry flies exhibit a peculiar behavior in which they repeatedly stray from, but then return to, the newly discovered resource. To study this behavior in more detail, we tracked hungry Drosophila as they explored a large arena, focusing on the question of how flies remain near the food. To determine whether flies use external stimuli, we individually eliminated visual, olfactory, and pheromonal cues. In all cases, flies still exhibited a centralized search behavior, suggesting that none of these cues are absolutely required for navigation back to the food. To simultaneously eliminate visual and olfactory cues associated with the position of the food, we constructed an apparatus in which the food could be rapidly translated from the center of the arena. Flies continued to search around the original location, even after the food was moved to a new position. A random search model based on measured locomotor statistics could not reproduce the centered nature of the animal's trajectory. We conclude that this behavior is best explained by a form of path integration in which the flies use idiothetic cues to search near the location of the food. We argue that the use of path integration to perform a centered local search is not a specialization of Drosophila but rather represents an ancient behavioral mode that is homologous to the more elaborate foraging strategies of central place foragers such as ants. Copyright © 2017 Elsevier Ltd. All rights reserved.
Path integral polymer propagator of relativistic and nonrelativistic particles
NASA Astrophysics Data System (ADS)
Morales-Técotl, Hugo A.; Rastgoo, Saeed; Ruelas, Juan C.
2017-03-01
A recent proposal to connect the loop quantization with the spin foam model for cosmology via the path integral is hereby adapted to the case of mechanical systems within the framework of the so-called polymer quantum mechanics. The mechanical models we consider are deparametrized and thus the group averaging technique is used to deal with the corresponding constraints. The transition amplitudes are written in a vertex expansion form used in the spin foam models, where here a vertex is actually a jump in position. Polymer propagators previously obtained by spectral methods for a nonrelativistic polymer particle, both free and in a box, are regained with this method and as a new result we obtain the polymer propagator of the relativistic particle. All of them reduce to their standard form in the continuum limit for which the length scale parameter of the polymer quantization is taken to be small. Our results are robust thanks to their analytic and exact character which in turn come from the fact that presented models are solvable. They lend support to the vertex expansion scheme of the polymer path integral explored before in a formal way for cosmological models. Some possible future developments are commented upon in the discussion.
Path integration mediated systematic search: a Bayesian model.
Vickerstaff, Robert J; Merkle, Tobias
2012-08-21
The systematic search behaviour is a backup system that increases the chances of desert ants finding their nest entrance after foraging when the path integrator has failed to guide them home accurately enough. Here we present a mathematical model of the systematic search that is based on extensive behavioural studies in North African desert ants Cataglyphis fortis. First, a simple search heuristic utilising Bayesian inference and a probability density function is developed. This model, which optimises the short-term nest detection probability, is then compared to three simpler search heuristics and to recorded search patterns of Cataglyphis ants. To compare the different searches a method to quantify search efficiency is established as well as an estimate of the error rate in the ants' path integrator. We demonstrate that the Bayesian search heuristic is able to automatically adapt to increasing levels of positional uncertainty to produce broader search patterns, just as desert ants do, and that it outperforms the three other search heuristics tested. The searches produced by it are also arguably the most similar in appearance to the ant's searches. Copyright © 2012 Elsevier Ltd. All rights reserved.
Path integral Monte Carlo on a lattice. II. Bound states
NASA Astrophysics Data System (ADS)
O'Callaghan, Mark; Miller, Bruce N.
2016-07-01
The equilibrium properties of a single quantum particle (qp) interacting with a classical gas for a wide range of temperatures that explore the system's behavior in the classical as well as in the quantum regime is investigated. Both the qp and the atoms are restricted to sites on a one-dimensional lattice. A path integral formalism developed within the context of the canonical ensemble is utilized, where the qp is represented by a closed, variable-step random walk on the lattice. Monte Carlo methods are employed to determine the system's properties. To test the usefulness of the path integral formalism, the Metropolis algorithm is employed to determine the equilibrium properties of the qp in the context of a square well potential, forcing the qp to occupy bound states. We consider a one-dimensional square well potential where all atoms on the lattice are occupied with one atom with an on-site potential except for a contiguous set of sites of various lengths centered at the middle of the lattice. Comparison of the potential energy, the energy fluctuations, and the correlation function are made between the results of the Monte Carlo simulations and the numerical calculations.
A note on the path integral representation for Majorana fermions
NASA Astrophysics Data System (ADS)
Greco, Andrés
2016-04-01
Majorana fermions are currently of huge interest in the context of nanoscience and condensed matter physics. Different to usual fermions, Majorana fermions have the property that the particle is its own anti-particle thus, they must be described by real fields. Mathematically, this property makes nontrivial the quantization of the problem due, for instance, to the absence of a Wick-like theorem. In view of the present interest on the subject, it is important to develop different theoretical approaches in order to study problems where Majorana fermions are involved. In this note we show that Majorana fermions can be studied in the context of field theories for constrained systems. Using the Faddeev-Jackiw formalism for quantum field theories with constraints, we derived the path integral representation for Majorana fermions. In order to show the validity of the path integral we apply it to an exactly solvable problem. This application also shows that it is rather simple to perform systematic calculations on the basis of the present framework.
Quantum-classical path integral. II. Numerical methodology
NASA Astrophysics Data System (ADS)
Lambert, Roberto; Makri, Nancy
2012-12-01
We present a quantum-classical methodology for propagating the density matrix of a system coupled to a polyatomic (large molecular or solvent) environment. The system is treated via a full path integral, while the dynamics of the environment is approximated in terms of classical trajectories. We obtain quantum-classical path integral (QCPI) expressions in which the trajectories can undergo transitions to other quantum states at regular time intervals, but the cumulative probability of these transitions is governed by the local strength of the state-to-state coupling as well as the magnitude of the solvent reorganization energy. If quantum effects in the coordinates of the environment are relatively weak, an inexpensive random hop approximation leads to accurate descriptions of the dynamics. We describe a systematic iterative scheme for including quantum mechanical corrections for the solvent by gradually accounting for nonlocal "quantum memory" effects. As the length of the included memory approaches the decoherence time of the environment, the iterative QCPI procedure converges to the full QCPI result. The methodology is illustrated with application to dissipative symmetric and asymmetric two-level systems.
Path-integral molecular dynamics simulation of diamond
NASA Astrophysics Data System (ADS)
Ramírez, Rafael; Herrero, Carlos P.; Hernández, Eduardo R.
2006-06-01
Diamond is studied by path-integral molecular dynamics simulations of the atomic nuclei in combination with a tight-binding Hamiltonian to describe its electronic structure and total energy. This approach allows us to quantify the influence of quantum zero-point vibrations and finite temperatures on both the electronic and vibrational properties of diamond. The electron-phonon coupling mediated by the zero-point vibration reduces the direct electronic gap of diamond by 10%. The calculated decrease of the direct gap with temperature shows good agreement with the experimental data available up to 700K . Anharmonic vibrational frequencies of the crystal have been obtained from a linear-response approach based on the path integral formalism. In particular, the temperature dependence of the zone-center optical phonon has been derived from the simulations. The anharmonicity of the interatomic potential produces a red shift of this phonon frequency. At temperatures above 500K , this shift is overestimated in comparison to available experimental data. The predicted temperature shift of the elastic constant c44 displays reasonable agreement with the available experimental results.
NASA Astrophysics Data System (ADS)
Wong, Kin-Yiu; Gao, Jiali
2007-12-01
Based on Kleinert's variational perturbation (KP) theory [Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets, 3rd ed. (World Scientific, Singapore, 2004)], we present an analytic path-integral approach for computing the effective centroid potential. The approach enables the KP theory to be applied to any realistic systems beyond the first-order perturbation (i.e., the original Feynman-Kleinert [Phys. Rev. A 34, 5080 (1986)] variational method). Accurate values are obtained for several systems in which exact quantum results are known. Furthermore, the computed kinetic isotope effects for a series of proton transfer reactions, in which the potential energy surfaces are evaluated by density-functional theory, are in good accordance with experiments. We hope that our method could be used by non-path-integral experts or experimentalists as a "black box" for any given system.
Potential theory, path integrals and the Laplacian of the indicator
NASA Astrophysics Data System (ADS)
Lange, Rutger-Jan
2012-11-01
This paper links the field of potential theory — i.e. the Dirichlet and Neumann problems for the heat and Laplace equation — to that of the Feynman path integral, by postulating the following seemingly ill-defined potential: V(x):=∓ {{σ^2}}/2nabla_x^2{1_{{xin D}}} where the volatility is the reciprocal of the mass (i.e. m = 1/ σ 2) and ħ = 1. The Laplacian of the indicator can be interpreted using the theory of distributions: it is the d-dimensional analogue of the Dirac δ'-function, which can formally be defined as partial_x^2{1_{x>0 }} . We show, first, that the path integral's perturbation series (or Born series) matches the classical single and double boundary layer series of potential theory, thereby connecting two hitherto unrelated fields. Second, we show that the perturbation series is valid for all domains D that allow Green's theorem (i.e. with a finite number of corners, edges and cusps), thereby expanding the classical applicability of boundary layers. Third, we show that the minus (plus) in the potential holds for the Dirichlet (Neumann) boundary condition; showing for the first time a particularly close connection between these two classical problems. Fourth, we demonstrate that the perturbation series of the path integral converges as follows:
Quantum Calisthenics: Gaussians, The Path Integral and Guided Numerical Approximations
Weinstein, Marvin; /SLAC
2009-02-12
It is apparent to anyone who thinks about it that, to a large degree, the basic concepts of Newtonian physics are quite intuitive, but quantum mechanics is not. My purpose in this talk is to introduce you to a new, much more intuitive way to understand how quantum mechanics works. I begin with an incredibly easy way to derive the time evolution of a Gaussian wave-packet for the case free and harmonic motion without any need to know the eigenstates of the Hamiltonian. This discussion is completely analytic and I will later use it to relate the solution for the behavior of the Gaussian packet to the Feynman path-integral and stationary phase approximation. It will be clear that using the information about the evolution of the Gaussian in this way goes far beyond what the stationary phase approximation tells us. Next, I introduce the concept of the bucket brigade approach to dealing with problems that cannot be handled totally analytically. This approach combines the intuition obtained in the initial discussion, as well as the intuition obtained from the path-integral, with simple numerical tools. My goal is to show that, for any specific process, there is a simple Hilbert space interpretation of the stationary phase approximation. I will then argue that, from the point of view of numerical approximations, the trajectory obtained from my generalization of the stationary phase approximation specifies that subspace of the full Hilbert space that is needed to compute the time evolution of the particular state under the full Hamiltonian. The prescription I will give is totally non-perturbative and we will see, by the grace of Maple animations computed for the case of the anharmonic oscillator Hamiltonian, that this approach allows surprisingly accurate computations to be performed with very little work. I think of this approach to the path-integral as defining what I call a guided numerical approximation scheme. After the discussion of the anharmonic oscillator I will
PhytoPath: an integrative resource for plant pathogen genomics
Pedro, Helder; Maheswari, Uma; Urban, Martin; Irvine, Alistair George; Cuzick, Alayne; McDowall, Mark D.; Staines, Daniel M.; Kulesha, Eugene; Hammond-Kosack, Kim Elizabeth; Kersey, Paul Julian
2016-01-01
PhytoPath (www.phytopathdb.org) is a resource for genomic and phenotypic data from plant pathogen species, that integrates phenotypic data for genes from PHI-base, an expertly curated catalog of genes with experimentally verified pathogenicity, with the Ensembl tools for data visualization and analysis. The resource is focused on fungi, protists (oomycetes) and bacterial plant pathogens that have genomes that have been sequenced and annotated. Genes with associated PHI-base data can be easily identified across all plant pathogen species using a BioMart-based query tool and visualized in their genomic context on the Ensembl genome browser. The PhytoPath resource contains data for 135 genomic sequences from 87 plant pathogen species, and 1364 genes curated for their role in pathogenicity and as targets for chemical intervention. Support for community annotation of gene models is provided using the WebApollo online gene editor, and we are working with interested communities to improve reference annotation for selected species. PMID:26476449
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2012-06-06
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Coupled exciton-photon Bose condensate in path integral formalism
NASA Astrophysics Data System (ADS)
Elistratov, A. A.; Lozovik, Yu. E.
2016-03-01
We study the behavior of exciton polaritons in an optical microcavity with an embedded semiconductor quantum well. We use a two-component exciton-photon approach formulated in terms of path integral formalism. In order to describe spatial distributions of the exciton and photon condensate densities, the two coupled equations of the Gross-Pitaevskii type are derived. For a homogeneous system, we find the noncondensate photon and exciton spectra, calculate the coefficients of transformation from the exciton-photon basis to the lower-upper polariton basis, and obtain the exciton and photon occupation numbers of the lower and upper polariton branches for nonzero temperatures. For an inhomogeneous system, the set of coupled equations of the Bogoliubov-de Gennes type is derived. The equations govern the spectra and spatial distributions of noncondensate photons and excitons.
Path integral quantization corresponding to the deformed Heisenberg algebra
Pramanik, Souvik; Moussa, Mohamed; Faizal, Mir; Ali, Ahmed Farag
2015-11-15
In this paper, the deformation of the Heisenberg algebra, consistent with both the generalized uncertainty principle and doubly special relativity, has been analyzed. It has been observed that, though this algebra can give rise to fractional derivative terms in the corresponding quantum mechanical Hamiltonian, a formal meaning can be given to them by using the theory of harmonic extensions of function. Depending on this argument, the expression of the propagator of the path integral corresponding to the deformed Heisenberg algebra, has been obtained. In particular, the consistent expression of the one dimensional free particle propagator has been evaluated explicitly. With this propagator in hand, it has been shown that, even in free particle case, normal generalized uncertainty principle and doubly special relativity show very much different result.
Path integral treatment of a noncentral electric potential
NASA Astrophysics Data System (ADS)
Ghoumaid, Ali; Benamira, Farid; Guechi, Larbi; Khiat, Zohra
2013-01-01
We present a rigorous path integral treatment of a dynamical system in the axially symmetric potential V(r,θ ) = V(r) + tfrac{1} {{r^2 }}V(θ ) . It is shown that the Green's function can be calculated in spherical coordinate system for V(θ ) = frac{{hbar ^2 }} {{2μ }}frac{{γ + β sin ^2 θ + α sin ^4 θ }} {{sin ^2 θ \\cos ^2 θ }} . As an illustration, we have chosen the example of a spherical harmonic oscillator and also the Coulomb potential for the radial dependence of this noncentral potential. The ring-shaped oscillator and the Hartmann ring-shaped potential are considered as particular cases. When α = β = γ = 0, the discrete energy spectrum, the normalized wave function of the spherical oscillator and the Coulomb potential of a hydrogen-like ion, for a state of orbital quantum number l ≥ 0, are recovered.
Hippocampal “Time Cells”: Time versus Path Integration
Kraus, Benjamin J.; Robinson, Robert J.; White, John A.; Eichenbaum, Howard; Hasselmo, Michael E.
2014-01-01
SUMMARY Recent studies have reported the existence of hippocampal “time cells,” neurons that fire at particular moments during periods when behavior and location are relatively constant. However, an alternative explanation of apparent time coding is that hippocampal neurons “path integrate” to encode the distance an animal has traveled. Here, we examined hippocampal neuronal firing patterns as rats ran in place on a treadmill, thus “clamping” behavior and location, while we varied the treadmill speed to distinguish time elapsed from distance traveled. Hippocampal neurons were strongly influenced by time and distance, and less so by minor variations in location. Furthermore, the activity of different neurons reflected integration over time and distance to varying extents, with most neurons strongly influenced by both factors and some significantly influenced by only time or distance. Thus, hippocampal neuronal networks captured both the organization of time and distance in a situation where these dimensions dominated an ongoing experience. PMID:23707613
Thermal Momentum Distribution from Path Integrals with Shifted Boundary Conditions
NASA Astrophysics Data System (ADS)
Giusti, Leonardo; Meyer, Harvey B.
2011-04-01
For a thermal field theory formulated in the grand canonical ensemble, the distribution of the total momentum is an observable characterizing the thermal state. We show that its cumulants are related to thermodynamic potentials. In a relativistic system, for instance, the thermal variance of the total momentum is a direct measure of the enthalpy. We relate the generating function of the cumulants to the ratio of (a) a partition function expressed as a Matsubara path integral with shifted boundary conditions in the compact direction and (b) the ordinary partition function. In this form the generating function is well suited for Monte Carlo evaluation, and the cumulants can be extracted straightforwardly. We test the method in the SU(3) Yang-Mills theory and obtain the entropy density at three different temperatures.
Path integral approach to electron scattering in classical electromagnetic potential
NASA Astrophysics Data System (ADS)
Chuang, Xu; Feng, Feng; Ying-Jun, Li
2016-05-01
As is known to all, the electron scattering in classical electromagnetic potential is one of the most widespread applications of quantum theory. Nevertheless, many discussions about electron scattering are based upon single-particle Schrodinger equation or Dirac equation in quantum mechanics rather than the method of quantum field theory. In this paper, by using the path integral approach of quantum field theory, we perturbatively evaluate the scattering amplitude up to the second order for the electron scattering by the classical electromagnetic potential. The results we derive are convenient to apply to all sorts of potential forms. Furthermore, by means of the obtained results, we give explicit calculations for the one-dimensional electric potential. Project supported by the National Natural Science Foundation of China (Grant Nos. 11374360, 11405266, and 11505285) and the National Basic Research Program of China (Grant No. 2013CBA01504).
Looping probabilities of elastic chains: a path integral approach.
Cotta-Ramusino, Ludovica; Maddocks, John H
2010-11-01
We consider an elastic chain at thermodynamic equilibrium with a heat bath, and derive an approximation to the probability density function, or pdf, governing the relative location and orientation of the two ends of the chain. Our motivation is to exploit continuum mechanics models for the computation of DNA looping probabilities, but here we focus on explaining the novel analytical aspects in the derivation of our approximation formula. Accordingly, and for simplicity, the current presentation is limited to the illustrative case of planar configurations. A path integral formalism is adopted, and, in the standard way, the first approximation to the looping pdf is obtained from a minimal energy configuration satisfying prescribed end conditions. Then we compute an additional factor in the pdf which encompasses the contributions of quadratic fluctuations about the minimum energy configuration along with a simultaneous evaluation of the partition function. The original aspects of our analysis are twofold. First, the quadratic Lagrangian describing the fluctuations has cross-terms that are linear in first derivatives. This, seemingly small, deviation from the structure of standard path integral examples complicates the necessary analysis significantly. Nevertheless, after a nonlinear change of variable of Riccati type, we show that the correction factor to the pdf can still be evaluated in terms of the solution to an initial value problem for the linear system of Jacobi ordinary differential equations associated with the second variation. The second novel aspect of our analysis is that we show that the Hamiltonian form of these linear Jacobi equations still provides the appropriate correction term in the inextensible, unshearable limit that is commonly adopted in polymer physics models of, e.g. DNA. Prior analyses of the inextensible case have had to introduce nonlinear and nonlocal integral constraints to express conditions on the relative displacement of the end
Age differences in virtual environment and real world path integration
Adamo, Diane E.; Briceño, Emily M.; Sindone, Joseph A.; Alexander, Neil B.; Moffat, Scott D.
2012-01-01
Accurate path integration (PI) requires the integration of visual, proprioceptive, and vestibular self-motion cues and age effects associated with alterations in processing information from these systems may contribute to declines in PI abilities. The present study investigated age-related differences in PI in conditions that varied as a function of available sources of sensory information. Twenty-two healthy, young (23.8 ± 3.0 years) and 16 older (70.1 ± 6.4 years) adults participated in distance reproduction and triangle completion tasks (TCTs) performed in a virtual environment (VE) and two “real world” conditions: guided walking and wheelchair propulsion. For walking and wheelchair propulsion conditions, participants wore a blindfold and wore noise-blocking headphones and were guided through the workspace by the experimenter. For the VE condition, participants viewed self-motion information on a computer monitor and used a joystick to navigate through the environment. For TCTs, older compared to younger individuals showed greater errors in rotation estimations performed in the wheelchair condition, and for rotation and distance estimations in the VE condition. Distance reproduction tasks (DRTs), in contrast, did not show any age effects. These findings demonstrate that age differences in PI vary as a function of the available sources of information and by the complexity of outbound pathway. PMID:23055969
NASA Astrophysics Data System (ADS)
LaChapelle, J.
1996-09-01
A new axiomatic formulation of path integrals is used to construct a path integral solution of the Schrödinger equation in curvilinear coordinates. An important feature of the formalism is that a coordinate transformation in the variables of the wavefunction does not imply a change of variable of integration in the path integral. Consequently, a transformation from Euclidean to curvilinear coordinates is simple to handle; there is no need to introduce ``quantum corrections'' into the action functional. Furthermore, the paths are differentiable: hence, issues related to stochastic paths do not arise. The procedure for constructing the path integral solution of the Schrödinger equation is straightforward. The case of the Schrödinger equation in spherical coordinates for a free particle is presented in detail.
NASA Astrophysics Data System (ADS)
Hogan, Patrick; Parajka, Juraj; Blöschl, Günter
2014-05-01
The eddy covariance method has become one of the most common methods for measuring evaporation and carbon dioxide fluxes as it makes direct measurements and can be used at different spatial scales. Eddy covariance measurement devices are divided into two different designs, designated open path and closed path depending on where the gas of interest is measured. There is currently no preferred eddy covariance design, with the decision on which design to use usually based on the local precipitation conditions and power availability. A recent long term field comparison by Haslwanter et al. (2009) found differences in the measured and corrected evaporation between the different designs, with the largest differences in the latent heat flux occurring during periods of above average meteorological conditions. All previous comparison studies have been performed using the LI-7500 OP analyser which must be placed a distance away from the closed path intake and the path of the sonic anemometer. This must be accounted for by including corrections for high frequency filtering and sensor heating. The objective of this study is to use the IRGASON open-path design from Campbell Scientific where the gas analyser and sonic anemometer will be directly aligned with the intake to a closed path sensor to compare the different sensor designs. The measurements will be performed at the HOAL catchment at Petzenkirchen, Austria, which is equipped with a weather and energy balance station as well as an extensive soil moisture network to measure evaporation. This project will perform a comparison between open path and closed path eddy covariance systems using a new integrated open path design. The measurements will then be used to study the differences between the corrections required for the different designs and the effects of meteorological variables on the measured latent heat fluxes to address the issue of open and closed path gas analyser comparisons.
The retrosplenial cortex is necessary for path integration in the dark.
Elduayen, Coralie; Save, Etienne
2014-10-01
An increasing amount of data indicates that the retrosplenial cortex (RSC) plays a role in navigation and spatial memory. Moreover, it has been suggested that the RSC integrates mnemonic spatial features of the environment with self-motion information therefore enabling accurate path integration in darkness. This hypothesis rests on data obtained from animals trained in spatial memory tasks involving the conjoint use of allothetic and idiothetic information [8]. We examined the contribution of the RSC when animals are submitted to a path integration task with minimal memory requirement in light and dark. We found that RSC-lesioned rats exhibited a path integration deficit in the dark but not in the light. This suggests that the RSC is important for path integration and incorporates visuospatial information to maintain path integration accuracy.
Keeping track of the distance from home by leaky integration along veering paths.
Lappe, Markus; Stiels, Maren; Frenz, Harald; Loomis, Jack M
2011-07-01
When humans use vision to gauge the travel distance of an extended forward movement, they often underestimate the movement's extent. This underestimation can be explained by leaky path integration, an integration of the movement to obtain distance. Distance underestimation occurs because this integration is imperfect and contains a leak that increases with distance traveled. We asked human observers to estimate the distance from a starting location for visually simulated movements in a virtual environment. The movements occurred along curved paths that veered left and right around a central forward direction. In this case, the distance that has to be integrated (i.e., the beeline distance between origin and endpoint) and the distance that is traversed (the path length along the curve) are distinct. We then tested whether the leak accumulated with distance from the origin or with traversed distance along the curved path. Leaky integration along the path makes the seemingly counterintuitive prediction that the estimated origin-to-endpoint distance should decrease with increasing veering, because the length of the path over which the integration occurs increases, leading to a larger leak effect. The results matched the prediction: movements of identical origin-to-endpoint distance were judged as shorter when the path became longer. We conclude that leaky path integration from visual motion is performed along the traversed path even when a straight beeline distance is calculated.
Quantum effects in graphene monolayers: Path-integral simulations.
Herrero, Carlos P; Ramírez, Rafael
2016-12-14
Path-integral molecular dynamics (PIMD) simulations have been carried out to study the influence of quantum dynamics of carbon atoms on the properties of a single graphene layer. Finite-temperature properties were analyzed in the range from 12 to 2000 K, by using the LCBOPII effective potential. To assess the magnitude of quantum effects in structural and thermodynamic properties of graphene, classical molecular dynamics simulations have been also performed. Particular emphasis has been laid on the atomic vibrations along the out-of-plane direction. Even though quantum effects are present in these vibrational modes, we show that at any finite temperature classical-like motion dominates over quantum delocalization, provided that the system size is large enough. Vibrational modes display an appreciable anharmonicity, as derived from a comparison between kinetic and potential energies of the carbon atoms. Nuclear quantum effects are found to be appreciable in the interatomic distance and layer area at finite temperatures. The thermal expansion coefficient resulting from PIMD simulations vanishes in the zero-temperature limit, in agreement with the third law of thermodynamics.
Computational Convergence of the Path Integral for Real Dendritic Morphologies
2012-01-01
Neurons are characterised by a morphological structure unique amongst biological cells, the core of which is the dendritic tree. The vast number of dendritic geometries, combined with heterogeneous properties of the cell membrane, continue to challenge scientists in predicting neuronal input-output relationships, even in the case of sub-threshold dendritic currents. The Green’s function obtained for a given dendritic geometry provides this functional relationship for passive or quasi-active dendrites and can be constructed by a sum-over-trips approach based on a path integral formalism. In this paper, we introduce a number of efficient algorithms for realisation of the sum-over-trips framework and investigate the convergence of these algorithms on different dendritic geometries. We demonstrate that the convergence of the trip sampling methods strongly depends on dendritic morphology as well as the biophysical properties of the cell membrane. For real morphologies, the number of trips to guarantee a small convergence error might become very large and strongly affect computational efficiency. As an alternative, we introduce a highly-efficient matrix method which can be applied to arbitrary branching structures. PMID:23174188
Path integral regularization of pure Yang-Mills theory
Jacquot, J. L.
2009-07-15
In enlarging the field content of pure Yang-Mills theory to a cutoff dependent matrix valued complex scalar field, we construct a vectorial operator, which is by definition invariant with respect to the gauge transformation of the Yang-Mills field and with respect to a Stueckelberg type gauge transformation of the scalar field. This invariant operator converges to the original Yang-Mills field as the cutoff goes to infinity. With the help of cutoff functions, we construct with this invariant a regularized action for the pure Yang-Mills theory. In order to be able to define both the gauge and scalar fields kinetic terms, other invariant terms are added to the action. Since the scalar fields flat measure is invariant under the Stueckelberg type gauge transformation, we obtain a regularized gauge-invariant path integral for pure Yang-Mills theory that is mathematically well defined. Moreover, the regularized Ward-Takahashi identities describing the dynamics of the gauge fields are exactly the same as the formal Ward-Takahashi identities of the unregularized theory.
Quantum effects in graphene monolayers: Path-integral simulations
NASA Astrophysics Data System (ADS)
Herrero, Carlos P.; Ramírez, Rafael
2016-12-01
Path-integral molecular dynamics (PIMD) simulations have been carried out to study the influence of quantum dynamics of carbon atoms on the properties of a single graphene layer. Finite-temperature properties were analyzed in the range from 12 to 2000 K, by using the LCBOPII effective potential. To assess the magnitude of quantum effects in structural and thermodynamic properties of graphene, classical molecular dynamics simulations have been also performed. Particular emphasis has been laid on the atomic vibrations along the out-of-plane direction. Even though quantum effects are present in these vibrational modes, we show that at any finite temperature classical-like motion dominates over quantum delocalization, provided that the system size is large enough. Vibrational modes display an appreciable anharmonicity, as derived from a comparison between kinetic and potential energies of the carbon atoms. Nuclear quantum effects are found to be appreciable in the interatomic distance and layer area at finite temperatures. The thermal expansion coefficient resulting from PIMD simulations vanishes in the zero-temperature limit, in agreement with the third law of thermodynamics.
Nearest neighbor interaction in the Path Integral Renormalization Group method
NASA Astrophysics Data System (ADS)
de Silva, Wasanthi; Clay, R. Torsten
2014-03-01
The Path Integral Renormalization Group (PIRG) method is an efficient numerical algorithm for studying ground state properties of strongly correlated electron systems. The many-body ground state wave function is approximated by an optimized linear combination of Slater determinants which satisfies the variational principle. A major advantage of PIRG is that is does not suffer the Fermion sign problem of quantum Monte Carlo. Results are exact in the noninteracting limit and can be enhanced using space and spin symmetries. Many observables can be calculated using Wick's theorem. PIRG has been used predominantly for the Hubbard model with a single on-site Coulomb interaction U. We describe an extension of PIRG to the extended Hubbard model (EHM) including U and a nearest-neighbor interaction V. The EHM is particularly important in models of charge-transfer solids (organic superconductors) and at 1/4-filling drives a charge-ordered state. The presence of lattice frustration also makes studying these systems difficult. We test the method with comparisons to small clusters and long one dimensional chains, and show preliminary results for a coupled-chain model for the (TMTTF)2X materials. This work was supported by DOE grant DE-FG02-06ER46315.
Isotope effects in ice Ih: a path-integral simulation.
Herrero, Carlos P; Ramírez, Rafael
2011-03-07
Ice Ih has been studied by path-integral molecular dynamics simulations, using the effective q-TIP4P/F potential model for flexible water. This has allowed us to analyze finite-temperature quantum effects in this solid phase from 25 to 300 K at ambient pressure. Among these effects we find a negative thermal expansion of ice at low temperatures, which does not appear in classical molecular dynamics simulations. The compressibility derived from volume fluctuations gives results in line with experimental data. We have analyzed isotope effects in ice Ih by considering normal, heavy, and tritiated water. In particular, we studied the effect of changing the isotopic mass of hydrogen on the kinetic energy and atomic delocalization in the crystal as well as on structural properties such as interatomic distances and molar volume. For D(2)O ice Ih at 100 K we obtained a decrease in molar volume and intramolecular O-H distance of 0.6% and 0.4%, respectively, as compared to H(2)O ice.
Path integral duality modified propagators in spacetimes with constant curvature
NASA Astrophysics Data System (ADS)
Kothawala, Dawood; Sriramkumar, L.; Shankaranarayanan, S.; Padmanabhan, T.
2009-08-01
The hypothesis of path integral duality provides a prescription to evaluate the propagator of a free, quantum scalar field in a given classical background, taking into account the existence of a fundamental length, say, the Planck length LP in a locally Lorentz invariant manner. We use this prescription to evaluate the duality modified propagators in spacetimes with constant curvature (exactly in the case of one spacetime, and in the Gaussian approximation for another two), and show that (i) the modified propagators are ultraviolet finite, (ii) the modifications are nonperturbative in LP, and (iii) LP seems to behave like a “zero point length” of spacetime intervals such that ⟨σ2(x,x')⟩=[σ2(x,x')+O(1)LP2], where σ(x,x') is the geodesic distance between the two spacetime points x and x', and the angular brackets denote (a suitable) average over the quantum gravitational fluctuations. We briefly discuss the implications of our results.
Barbero-Immirzi parameter, manifold invariants and Euclidean path integrals
NASA Astrophysics Data System (ADS)
Liko, Tomáš
2012-05-01
The Barbero-Immirzi parameter γ appears in the real connection formulation of gravity in terms of the Ashtekar variables, and gives rise to a one-parameter quantization ambiguity in loop quantum gravity. In this paper, we investigate the conditions under which γ will have physical effects in Euclidean quantum gravity. This is done by constructing a well-defined Euclidean path integral for the Holst action with a non-zero cosmological constant on a manifold with a boundary. We find that two general conditions must be satisfied by the spacetime manifold in order for the Holst action and its surface integral to be non-zero: (i) the metric has to be non-diagonalizable; (ii) the Pontryagin number of the manifold has to be non-zero. The latter is a strong topological condition and rules out many of the known solutions to the Einstein field equations. This result leads us to evaluate the on-shell first-order Holst action and corresponding Euclidean partition function on the Taub-NUT-ADS solution. We find that γ shows up as a finite rotation of the on-shell partition function which corresponds to shifts in the energy and entropy of the NUT charge. In an appendix, we also evaluate the Holst action on the Taub-NUT and Taub-bolt solutions in flat spacetime and find that in that case as well γ shows up in the energy and entropy of the NUT and bolt charges. We also present an example whereby the Euler characteristic of the manifold has a non-trivial effect on black hole mergers. Communicated by PRLV Moniz
Path-integral approach to 't Hooft's derivation of quantum physics from classical physics
Blasone, Massimo; Jizba, Petr; Kleinert, Hagen
2005-05-15
We present a path-integral formulation of 't Hooft's derivation of quantum physics from classical physics. The crucial ingredient of this formulation is Gozzi et al.'s supersymmetric path integral of classical mechanics. We quantize explicitly two simple classical systems: the planar mathematical pendulum and the Roessler dynamical system.
Factors Affecting Counselor Educators' Integration of Educational Technology: A Path Analysis
ERIC Educational Resources Information Center
Kennedy, John F.
2011-01-01
This study used path analysis to explore the effects of individual and institutional-level factors on counselor educators' integration of technology in counselor education. The study fills a gap in the literature by providing a research-based path model describing counselor educators' integration of technology in counselor education. Counselor…
Factors Affecting Counselor Educators' Integration of Educational Technology: A Path Analysis
ERIC Educational Resources Information Center
Kennedy, John F.
2011-01-01
This study used path analysis to explore the effects of individual and institutional-level factors on counselor educators' integration of technology in counselor education. The study fills a gap in the literature by providing a research-based path model describing counselor educators' integration of technology in counselor education. Counselor…
Color path-integral Monte Carlo simulations of quark-gluon plasma
NASA Astrophysics Data System (ADS)
Filinov, V. S.; Ivanov, Yu. B.; Bonitz, M.; Fortov, V. E.; Levashov, P. R.
2012-02-01
Thermodynamic properties of a strongly coupled quark-gluon plasma (QGP) of constituent quasiparticles are studied by a color path-integral Monte Carlo simulations (CPIMC). For our simulations we have presented QGP partition function in the form of color path integral with new relativistic measure instead of Gaussian one used in Feynman and Wiener path integrals. For integration over color variable we have also developed procedure of sampling color variables according to the group SU(3) Haar measure. It is shown that this method is able to reproduce the available quantum lattice chromodynamics (QCD) data.
NASA Astrophysics Data System (ADS)
Haftbaradaran, Hamed; Qu, Jianmin
2014-11-01
In this study, we first demonstrate that the J-integral in classical linear elasticity becomes path-dependent when the solid is subjected to combined electrical, chemical and mechanical loadings. We then construct an electro-chemo-mechanical J-integral that is path-independent under such combined multiple driving forces. Further, we show that this electro-chemo-mechanical J-integral represents the rate at which the grand potential releases per unit crack growth. As an example, the path-independent nature of the electro-chemo-mechanical J-integral is demonstrated by solving the problem of a thin elastic film delaminated from a thick elastic substrate.
Quantum circuit dynamics via path integrals: Is there a classical action for discrete-time paths?
NASA Astrophysics Data System (ADS)
Penney, Mark D.; Enshan Koh, Dax; Spekkens, Robert W.
2017-07-01
It is straightforward to compute the transition amplitudes of a quantum circuit using the sum-over-paths methodology when the gates in the circuit are balanced, where a balanced gate is one for which all non-zero transition amplitudes are of equal magnitude. Here we consider the question of whether, for such circuits, the relative phases of different discrete-time paths through the configuration space can be defined in terms of a classical action, as they are for continuous-time paths. We show how to do so for certain kinds of quantum circuits, namely, Clifford circuits where the elementary systems are continuous-variable systems or discrete systems of odd-prime dimension. These types of circuit are distinguished by having phase-space representations that serve to define their classical counterparts. For discrete systems, the phase-space coordinates are also discrete variables. We show that for each gate in the generating set, one can associate a symplectomorphism on the phase-space and to each of these one can associate a generating function, defined on two copies of the configuration space. For discrete systems, the latter association is achieved using tools from algebraic geometry. Finally, we show that if the action functional for a discrete-time path through a sequence of gates is defined using the sum of the corresponding generating functions, then it yields the correct relative phases for the path-sum expression. These results are likely to be relevant for quantizing physical theories where time is fundamentally discrete, characterizing the classical limit of discrete-time quantum dynamics, and proving complexity results for quantum circuits.
Square-root actions, metric signature, and the path integral of quantum gravity
NASA Astrophysics Data System (ADS)
Carlini, A.; Greensite, J.
1995-12-01
We consider quantization of the Baierlein-Sharp-Wheeler form of the gravitational action, in which the lapse function is determined from the Hamiltonian constraint. This action has a square root form, analogous to the actions of the relativistic particle and Nambu string. We argue that path-integral quantization of the gravitational action should be based on a path integrand exp[ √i S] rather than the familiar Feynman expression exp[iS], and that unitarity requires integration over manifolds of both Euclidean and Lorentzian signature. We discuss the relation of this path integral to our previous considerations regarding the problem of time, and extend our approach to include fermions.
Piloting and Path Integration within and across Boundaries
ERIC Educational Resources Information Center
Mou, Weimin; Wang, Lin
2015-01-01
Three experiments investigated whether navigation is less efficient across boundaries than within boundaries. In an immersive virtual environment, participants learned objects' locations in a large room or a small room. Participants then pointed to the objects' original locations after physically walking a circuitous path without vision.…
Piloting and Path Integration within and across Boundaries
ERIC Educational Resources Information Center
Mou, Weimin; Wang, Lin
2015-01-01
Three experiments investigated whether navigation is less efficient across boundaries than within boundaries. In an immersive virtual environment, participants learned objects' locations in a large room or a small room. Participants then pointed to the objects' original locations after physically walking a circuitous path without vision.…
PathCase-SB: integrating data sources and providing tools for systems biology research
2012-01-01
Background Integration of metabolic pathways resources and metabolic network models, and deploying new tools on the integrated platform can help perform more effective and more efficient systems biology research on understanding the regulation of metabolic networks. Therefore, the tasks of (a) integrating under a single database environment regulatory metabolic networks and existing models, and (b) building tools to help with modeling and analysis are desirable and intellectually challenging computational tasks. Results PathCase Systems Biology (PathCase-SB) is built and released. This paper describes PathCase-SB user interfaces developed to date. The current PathCase-SB system provides a database-enabled framework and web-based computational tools towards facilitating the development of kinetic models for biological systems. PathCase-SB aims to integrate systems biology models data and metabolic network data of selected biological data sources on the web (currently, BioModels Database and KEGG, respectively), and to provide more powerful and/or new capabilities via the new web-based integrative framework. Conclusions Each of the current four PathCase-SB interfaces, namely, Browser, Visualization, Querying, and Simulation interfaces, have expanded and new capabilities as compared with the original data sources. PathCase-SB is already available on the web and being used by researchers across the globe. PMID:22697505
NASA Astrophysics Data System (ADS)
Fine, Dana S.; Sawin, Stephen
2017-01-01
Feynman's time-slicing construction approximates the path integral by a product, determined by a partition of a finite time interval, of approximate propagators. This paper formulates general conditions to impose on a short-time approximation to the propagator in a general class of imaginary-time quantum mechanics on a Riemannian manifold which ensure that these products converge. The limit defines a path integral which agrees pointwise with the heat kernel for a generalized Laplacian. The result is a rigorous construction of the propagator for supersymmetric quantum mechanics, with potential, as a path integral. Further, the class of Laplacians includes the square of the twisted Dirac operator, which corresponds to an extension of N = 1/2 supersymmetric quantum mechanics. General results on the rate of convergence of the approximate path integrals suffice in this case to derive the local version of the Atiyah-Singer index theorem.
A brief view of known landmarks reorientates path integration in hamsters
NASA Astrophysics Data System (ADS)
Etienne, A. S.; Boulens, V.; Maurer, R.; Rowe, T.; Siegrist, C.
In darkness, hamsters commute between their nest and a feeding site through path integration only, and therefore show cumulative errors in the return direction to the nest. We examined whether a brief presentation of familiar room cues could reset the path integrator. The hamsters could see the room cues either during, or at the end of, the outward journey to the food place, in a conflict situation where motion cues and visual information were set at variance. In both conditions, the animals used mainly visual information to return home. Thus, hamsters can determine their azimuth, and possibly their location, through a visual fix, and can reset their path integrator through the fix. This allows them to update their position during further locomotion in the dark and thus to compute a correct homing vector with respect to a visually induced reference frame. Taking episodic positional fixes may greatly enhance the functional value of path integration.
A simple and accurate algorithm for path integral molecular dynamics with the Langevin thermostat
NASA Astrophysics Data System (ADS)
Liu, Jian; Li, Dezhang; Liu, Xinzijian
2016-07-01
We introduce a novel simple algorithm for thermostatting path integral molecular dynamics (PIMD) with the Langevin equation. The staging transformation of path integral beads is employed for demonstration. The optimum friction coefficients for the staging modes in the free particle limit are used for all systems. In comparison to the path integral Langevin equation thermostat, the new algorithm exploits a different order of splitting for the phase space propagator associated to the Langevin equation. While the error analysis is made for both algorithms, they are also employed in the PIMD simulations of three realistic systems (the H2O molecule, liquid para-hydrogen, and liquid water) for comparison. It is shown that the new thermostat increases the time interval of PIMD by a factor of 4-6 or more for achieving the same accuracy. In addition, the supplementary material shows the error analysis made for the algorithms when the normal-mode transformation of path integral beads is used.
A simple and accurate algorithm for path integral molecular dynamics with the Langevin thermostat.
Liu, Jian; Li, Dezhang; Liu, Xinzijian
2016-07-14
We introduce a novel simple algorithm for thermostatting path integral molecular dynamics (PIMD) with the Langevin equation. The staging transformation of path integral beads is employed for demonstration. The optimum friction coefficients for the staging modes in the free particle limit are used for all systems. In comparison to the path integral Langevin equation thermostat, the new algorithm exploits a different order of splitting for the phase space propagator associated to the Langevin equation. While the error analysis is made for both algorithms, they are also employed in the PIMD simulations of three realistic systems (the H2O molecule, liquid para-hydrogen, and liquid water) for comparison. It is shown that the new thermostat increases the time interval of PIMD by a factor of 4-6 or more for achieving the same accuracy. In addition, the supplementary material shows the error analysis made for the algorithms when the normal-mode transformation of path integral beads is used.
Rotational error in path integration: encoding and execution errors in angle reproduction.
Chrastil, Elizabeth R; Warren, William H
2017-03-16
Path integration is fundamental to human navigation. When a navigator leaves home on a complex outbound path, they are able to keep track of their approximate position and orientation and return to their starting location on a direct homebound path. However, there are several sources of error during path integration. Previous research has focused almost exclusively on encoding error-the error in registering the outbound path in memory. Here, we also consider execution error-the error in the response, such as turning and walking a homebound trajectory. In two experiments conducted in ambulatory virtual environments, we examined the contribution of execution error to the rotational component of path integration using angle reproduction tasks. In the reproduction tasks, participants rotated once and then rotated again to face the original direction, either reproducing the initial turn or turning through the supplementary angle. One outstanding difficulty in disentangling encoding and execution error during a typical angle reproduction task is that as the encoding angle increases, so does the required response angle. In Experiment 1, we dissociated these two variables by asking participants to report each encoding angle using two different responses: by turning to walk on a path parallel to the initial facing direction in the same (reproduction) or opposite (supplementary angle) direction. In Experiment 2, participants reported the encoding angle by turning both rightward and leftward onto a path parallel to the initial facing direction, over a larger range of angles. The results suggest that execution error, not encoding error, is the predominant source of error in angular path integration. These findings also imply that the path integrator uses an intrinsic (action-scaled) rather than an extrinsic (objective) metric.
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Which way and how far? Tracking of translation and rotation information for human path integration.
Chrastil, Elizabeth R; Sherrill, Katherine R; Hasselmo, Michael E; Stern, Chantal E
2016-10-01
Path integration, the constant updating of the navigator's knowledge of position and orientation during movement, requires both visuospatial knowledge and memory. This study aimed to develop a systems-level understanding of human path integration by examining the basic building blocks of path integration in humans. To achieve this goal, we used functional imaging to examine the neural mechanisms that support the tracking and memory of translational and rotational components of human path integration. Critically, and in contrast to previous studies, we examined movement in translation and rotation tasks with no defined end-point or goal. Navigators accumulated translational and rotational information during virtual self-motion. Activity in hippocampus, retrosplenial cortex (RSC), and parahippocampal cortex (PHC) increased during both translation and rotation encoding, suggesting that these regions track self-motion information during path integration. These results address current questions regarding distance coding in the human brain. By implementing a modified delayed match to sample paradigm, we also examined the encoding and maintenance of path integration signals in working memory. Hippocampus, PHC, and RSC were recruited during successful encoding and maintenance of path integration information, with RSC selective for tasks that required processing heading rotation changes. These data indicate distinct working memory mechanisms for translation and rotation, which are essential for updating neural representations of current location. The results provide evidence that hippocampus, PHC, and RSC flexibly track task-relevant translation and rotation signals for path integration and could form the hub of a more distributed network supporting spatial navigation. Hum Brain Mapp 37:3636-3655, 2016. © 2016 Wiley Periodicals, Inc.
A variational path integral molecular dynamics study of a solid helium-4
NASA Astrophysics Data System (ADS)
Miura, Shinichi
2011-01-01
In the present study, a variational path integral molecular dynamics method developed by the author [Chem. Phys. Lett. 482 (2009) 165] is applied to a solid helium-4 in the ground state. The method is a molecular dynamics algorithm for a variational path integral method which can be used to generate the exact ground state numerically. The solid state is shown to successfully be realized by the method, although a poor trial wavefunction that cannot describe the solid state is used.
Pérez, Alejandro; von Lilienfeld, O Anatole
2011-08-09
Thermodynamic integration, perturbation theory, and λ-dynamics methods were applied to path integral molecular dynamics calculations to investigate free energy differences due to "alchemical" transformations. Several estimators were formulated to compute free energy differences in solvable model systems undergoing changes in mass and/or potential. Linear and nonlinear alchemical interpolations were used for the thermodynamic integration. We find improved convergence for the virial estimators, as well as for the thermodynamic integration over nonlinear interpolation paths. Numerical results for the perturbative treatment of changes in mass and electric field strength in model systems are presented. We used thermodynamic integration in ab initio path integral molecular dynamics to compute the quantum free energy difference of the isotope transformation in the Zundel cation. The performance of different free energy methods is discussed.
An Anatomically Constrained Model for Path Integration in the Bee Brain.
Stone, Thomas; Webb, Barbara; Adden, Andrea; Weddig, Nicolai Ben; Honkanen, Anna; Templin, Rachel; Wcislo, William; Scimeca, Luca; Warrant, Eric; Heinze, Stanley
2017-10-04
Path integration is a widespread navigational strategy in which directional changes and distance covered are continuously integrated on an outward journey, enabling a straight-line return to home. Bees use vision for this task-a celestial-cue-based visual compass and an optic-flow-based visual odometer-but the underlying neural integration mechanisms are unknown. Using intracellular electrophysiology, we show that polarized-light-based compass neurons and optic-flow-based speed-encoding neurons converge in the central complex of the bee brain, and through block-face electron microscopy, we identify potential integrator cells. Based on plausible output targets for these cells, we propose a complete circuit for path integration and steering in the central complex, with anatomically identified neurons suggested for each processing step. The resulting model circuit is thus fully constrained biologically and provides a functional interpretation for many previously unexplained architectural features of the central complex. Moreover, we show that the receptive fields of the newly discovered speed neurons can support path integration for the holonomic motion (i.e., a ground velocity that is not precisely aligned with body orientation) typical of bee flight, a feature not captured in any previously proposed model of path integration. In a broader context, the model circuit presented provides a general mechanism for producing steering signals by comparing current and desired headings-suggesting a more basic function for central complex connectivity, from which path integration may have evolved. Copyright © 2017 Elsevier Ltd. All rights reserved.
Phase-space path-integral calculation of the Wigner function
NASA Astrophysics Data System (ADS)
Samson, J. H.
2003-10-01
The Wigner function W(q, p) is formulated as a phase-space path integral, whereby its sign oscillations can be seen to follow from interference between the geometrical phases of the paths. The approach has similarities to the path-centroid method in the configuration-space path integral. Paths can be classified by the midpoint of their ends; short paths where the midpoint is close to (q, p) and which lie in regions of low energy (low P function of the Hamiltonian) will dominate, and the enclosed area will determine the sign of the Wigner function. As a demonstration, the method is applied to a sequence of density matrices interpolating between a Poissonian number distribution and a number state, each member of which can be represented exactly by a discretized path integral with a finite number of vertices. Saddle-point evaluation of these integrals recovers (up to a constant factor) the WKB approximation to the Wigner function of a number state.
Trouvé, Hélène; Couturier, Yves; Etheridge, Francis; Saint-Jean, Olivier; Somme, Dominique
2010-01-01
Background The literature on integration indicates the need for an enhanced theorization of institutional integration. This article proposes path dependence as an analytical framework to study the systems in which integration takes place. Purpose PRISMA proposes a model for integrating health and social care services for older adults. This model was initially tested in Quebec. The PRISMA France study gave us an opportunity to analyze institutional integration in France. Methods A qualitative approach was used. Analyses were based on semi-structured interviews with actors of all levels of decision-making, observations of advisory board meetings, and administrative documents. Results Our analyses revealed the complexity and fragmentation of institutional integration. The path dependency theory, which analyzes the change capacity of institutions by taking into account their historic structures, allows analysis of this situation. The path dependency to the Bismarckian system and the incomplete reforms of gerontological policies generate the coexistence and juxtaposition of institutional systems. In such a context, no institution has sufficient ability to determine gerontology policy and build institutional integration by itself. Conclusion Using path dependence as an analytical framework helps to understand the reasons why institutional integration is critical to organizational and clinical integration, and the complex construction of institutional integration in France. PMID:20689740
Wang, Qian; Hammes-Schiffer, Sharon
2006-11-14
A hybrid quantum/classical path integral Monte Carlo (QC-PIMC) method for calculating the quantum free energy barrier for hydrogen transfer reactions in condensed phases is presented. In this approach, the classical potential of mean force along a collective reaction coordinate is calculated using umbrella sampling techniques in conjunction with molecular dynamics trajectories propagated according to a mapping potential. The quantum contribution is determined for each configuration along the classical trajectory with path integral Monte Carlo calculations in which the beads move according to an effective mapping potential. This type of path integral calculation does not utilize the centroid constraint and can lead to more efficient sampling of the relevant region of conformational space than free-particle path integral sampling. The QC-PIMC method is computationally practical for large systems because the path integral sampling for the quantum nuclei is performed separately from the classical molecular dynamics sampling of the entire system. The utility of the QC-PIMC method is illustrated by an application to hydride transfer in the enzyme dihydrofolate reductase. A comparison of this method to the quantized classical path and grid-based methods for this system is presented.
The development of path integration: combining estimations of distance and heading.
Smith, Alastair D; McKeith, Laura; Howard, Christina J
2013-12-01
Efficient daily navigation is underpinned by path integration, the mechanism by which we use self-movement information to update our position in space. This process is well understood in adulthood, but there has been relatively little study of path integration in childhood, leading to an underrepresentation in accounts of navigational development. Previous research has shown that calculation of distance and heading both tend to be less accurate in children as they are in adults, although there have been no studies of the combined calculation of distance and heading that typifies naturalistic path integration. In the present study, 5-year-olds and 7-year-olds took part in a triangle-completion task, where they were required to return to the start point of a multi-element path using only idiothetic information. Performance was compared to a sample of adult participants, who were found to be more accurate than children on measures of landing error, heading error, and distance error. Seven-year-olds were significantly more accurate than 5-year-olds on measures of landing error and heading error, although the difference between groups was much smaller for distance error. All measures were reliably correlated with age, demonstrating a clear development of path integration abilities within the age range tested. Taken together, these data make a strong case for the inclusion of path integration within developmental models of spatial navigational processing.
Quantum-classical path integral. I. Classical memory and weak quantum nonlocality.
Lambert, Roberto; Makri, Nancy
2012-12-14
We consider rigorous path integral descriptions of the dynamics of a quantum system coupled to a polyatomic environment, assuming that the latter is well approximated by classical trajectories. Earlier work has derived semiclassical or purely classical expressions for the influence functional from the environment, which should be sufficiently accurate for many situations, but the evaluation of quantum-(semi)classical path integral (QCPI) expressions has not been practical for large-scale simulation because the interaction with the environment introduces couplings nonlocal in time. In this work, we analyze the nature of the effects on a system from its environment in light of the observation [N. Makri, J. Chem. Phys. 109, 2994 (1998)] that true nonlocality in the path integral is a strictly quantum mechanical phenomenon. If the environment is classical, the path integral becomes local and can be evaluated in a stepwise fashion along classical trajectories of the free solvent. This simple "classical path" limit of QCPI captures fully the decoherence of the system via a classical mechanism. Small corrections to the classical path QCPI approximation may be obtained via an inexpensive random hop QCPI model, which accounts for some "back reaction" effects. Exploiting the finite length of nonlocality, we argue that further inclusion of quantum decoherence is possible via an iterative evaluation of the path integral. Finally, we show that the sum of the quantum amplitude factors with respect to the system paths leads to a smooth integrand as a function of trajectory initial conditions, allowing the use of Monte Carlo methods for the multidimensional phase space integral.
Bennett, Ilana J.; Stark, Craig E.L.
2015-01-01
Pattern separation describes the orthogonalization of similar inputs into unique, non-overlapping representations. This computational process is thought to serve memory by reducing interference and to be mediated by the dentate gyrus of the hippocampus. Using ultra-high in-plane resolution diffusion tensor imaging (hrDTI) in older adults, we previously demonstrated that integrity of the perforant path, which provides input to the dentate gyrus from entorhinal cortex, was associated with mnemonic discrimination, a behavioral outcome designed to load on pattern separation. The current hrDTI study assessed the specificity of this perforant path integrity-mnemonic discrimination relationship relative to other cognitive constructs (identified using a factor analysis) and white matter tracts (hippocampal cingulum, fornix, corpus callosum) in 112 healthy adults (20–87 years). Results revealed age-related declines in integrity of the perforant path and other medial temporal lobe (MTL) tracts (hippocampal cingulum, fornix). Controlling for global effects of brain aging, perforant path integrity related only to the factor that captured mnemonic discrimination performance. Comparable integrity-mnemonic discrimination relationships were also observed for the hippocampal cingulum and fornix. Thus, whereas perforant path integrity specifically relates to mnemonic discrimination, mnemonic discrimination may be mediated by a broader MTL network. PMID:26149893
Bennett, Ilana J; Stark, Craig E L
2016-03-01
Pattern separation describes the orthogonalization of similar inputs into unique, non-overlapping representations. This computational process is thought to serve memory by reducing interference and to be mediated by the dentate gyrus of the hippocampus. Using ultra-high in-plane resolution diffusion tensor imaging (hrDTI) in older adults, we previously demonstrated that integrity of the perforant path, which provides input to the dentate gyrus from entorhinal cortex, was associated with mnemonic discrimination, a behavioral outcome designed to load on pattern separation. The current hrDTI study assessed the specificity of this perforant path integrity-mnemonic discrimination relationship relative to other cognitive constructs (identified using a factor analysis) and white matter tracts (hippocampal cingulum, fornix, corpus callosum) in 112 healthy adults (20-87 years). Results revealed age-related declines in integrity of the perforant path and other medial temporal lobe (MTL) tracts (hippocampal cingulum, fornix). Controlling for global effects of brain aging, perforant path integrity related only to the factor that captured mnemonic discrimination performance. Comparable integrity-mnemonic discrimination relationships were also observed for the hippocampal cingulum and fornix. Thus, whereas perforant path integrity specifically relates to mnemonic discrimination, mnemonic discrimination may be mediated by a broader MTL network.
Feynman-Kac Path Integral Calculation of the Ground State Energy of Atoms
NASA Astrophysics Data System (ADS)
Orr, David Edwin
In a paper written in 1950, the mathematician, Marc Kac, established a rigorous basis for the Feynman path-integral formulation of quantum mechanics. The original Feynman path integral lacks mathematical rigor in the definition of "summing over all paths", which are infinite in number (a theorem by Cameron states that a finite, real or complex, Lebesgue measure of the path defined by Feynman does not exist). The difficulty of using Feynman's method in a computation is supported by the observation that an accurate path integral solution of the hydrogen groundstate was only recently computed (in 1984). Since its introduction in 1950, the Feynman-Kac path integral (FKPI) has received limited attention despite its simplicity and power in solving quantum many-body problems. This work demonstrates that the FKPI method can be used to find the groundstate and excited states of small atomic systems to within experimental accuracy, and is ideally suited for the new massively parallel computer architectures, such as the Thinking Machines CM-5, the INTEL Paragon, et al., or, can be effectively used in a cluster of loosely -coupled workstations. It also demonstrates a simple procedure for incorporating into the FKPI computational method restrictions on the many-body wavefunction imposed by permutation symmetries of identical particles.
Quantum-classical path integral with self-consistent solvent-driven reference propagators.
Banerjee, Tuseeta; Makri, Nancy
2013-10-24
Efficient procedures for evaluating the quantum-classical path integral (QCPI) [J. Chem. Phys. 2013, 137, 22A552] are described. The main idea is to identify a trajectory-specific reference Hamiltonian that captures the dominant effects of the classical "solvent" degrees of freedom on the dynamics of the quantum "system". This time-dependent reference is used to construct a system propagator that is valid for large time increments. Residual "quantum memory" interactions are included via the path integral representation of the density matrix, which converges with large time steps. Two physically motivated reference schemes are considered. The first involves the dynamics of the solvent unperturbed by the system, which forms the basis for the "classical path" approximation. The second is based on solvent trajectories determined self-consistently with the evolution of the system, according to the time-dependent self-consistent field or Ehrenfest model. Application to dissipative two-level systems indicates that both reference schemes allow a substantial increase of the path integral time step, leading to rapid convergence of the path sum. In addition, the time-dependent reference propagators automatically weigh state-to-state coupling against solvent reorganization in the determination of transition probabilities, further enhancing the convergence of the path integral.
Application of path-independent integrals to elevated temperature crack growth
NASA Technical Reports Server (NTRS)
Kim, K. S.; Van Stone, R. H.
1990-01-01
The applicability of the J-integral in elasto-plastic fracture mechanics is limited to isothermal, monotonic loading conditions from the theoretical viewpoint, while in many applications, for instance gas turbine engines, crack growth occurs in the presence of cyclic inelastic loading, thermomechanical loading and temperature gradients. A number of path-independent (P-I) integrals have been proposed which do not have the restrictions of the J-integral. A review indicates that four of these integrals, although they are not the classical conservation integrals, are path-independent under these complex loading conditions. This paper describes a combined analytical and experimental effort to evaluate the ability of these four P-I integrals to correlate the crack growth data of Alloy 718 at elevated temperatures. Results for uniform temperature, 538 C, cases indicate that all these integrals are capable of correlating the crack growth data over a wide range of cyclic plasticity.
Factor Ordering and Path Integral Measure for Quantum Gravity in (1+1) Dimensions
NASA Astrophysics Data System (ADS)
Haga, John; Maitra, Rachel Lash
2017-06-01
We develop a mathematically rigorous path integral representation of the time evolution operator for a model of (1+1) quantum gravity that incorporates factor ordering ambiguity. In obtaining a suitable integral kernel for the time-evolution operator, one requires that the corresponding Hamiltonian is self-adjoint; this issue is subtle for a particular category of factor orderings. We identify and parametrize a complete set of self-adjoint extensions and provide a canonical description of these extensions in terms of boundary conditions. Moreover, we use Trotter-type product formulae to construct path-integral representations of time evolution.
Automatic Tool Path Generation for Robot Integrated Surface Sculpturing System
NASA Astrophysics Data System (ADS)
Zhu, Jiang; Suzuki, Ryo; Tanaka, Tomohisa; Saito, Yoshio
In this paper, a surface sculpturing system based on 8-axis robot is proposed, the CAD/CAM software and tool path generation algorithm for this sculpturing system are presented. The 8-axis robot is composed of a 6-axis manipulator and a 2-axis worktable, it carves block of polystyrene foams by heated cutting tools. Multi-DOF (Degree of Freedom) robot benefits from the faster fashion than traditional RP (Rapid Prototyping) methods and more flexibility than CNC machining. With its flexibility driven from an 8-axis configuration, as well as efficient custom-developed software for rough cutting and finish cutting, this surface sculpturing system can carve sculptured surface accurately and efficiently.
NASA Astrophysics Data System (ADS)
Utama, Briandhika; Purqon, Acep
2016-08-01
Path Integral is a method to transform a function from its initial condition to final condition through multiplying its initial condition with the transition probability function, known as propagator. At the early development, several studies focused to apply this method for solving problems only in Quantum Mechanics. Nevertheless, Path Integral could also apply to other subjects with some modifications in the propagator function. In this study, we investigate the application of Path Integral method in financial derivatives, stock options. Black-Scholes Model (Nobel 1997) was a beginning anchor in Option Pricing study. Though this model did not successfully predict option price perfectly, especially because its sensitivity for the major changing on market, Black-Scholes Model still is a legitimate equation in pricing an option. The derivation of Black-Scholes has a high difficulty level because it is a stochastic partial differential equation. Black-Scholes equation has a similar principle with Path Integral, where in Black-Scholes the share's initial price is transformed to its final price. The Black-Scholes propagator function then derived by introducing a modified Lagrange based on Black-Scholes equation. Furthermore, we study the correlation between path integral analytical solution and Monte-Carlo numeric solution to find the similarity between this two methods.
A path-integral Langevin equation treatment of low-temperature doped helium clusters
NASA Astrophysics Data System (ADS)
Ing, Christopher; Hinsen, Konrad; Yang, Jing; Zeng, Toby; Li, Hui; Roy, Pierre-Nicholas
2012-06-01
We present an implementation of path integral molecular dynamics for sampling low temperature properties of doped helium clusters using Langevin dynamics. The robustness of the path integral Langevin equation and white-noise Langevin equation [M. Ceriotti, M. Parrinello, T. E. Markland, and D. E. Manolopoulos, J. Chem. Phys. 133, 124104 (2010)], 10.1063/1.3489925 sampling methods are considered for those weakly bound systems with comparison to path integral Monte Carlo (PIMC) in terms of efficiency and accuracy. Using these techniques, convergence studies are performed to confirm the systematic error reduction introduced by increasing the number of discretization steps of the path integral. We comment on the structural and energetic evolution of HeN-CO2 clusters from N = 1 to 20. To quantify the importance of both rotations and exchange in our simulations, we present a chemical potential and calculated band origin shifts as a function of cluster size utilizing PIMC sampling that includes these effects. This work also serves to showcase the implementation of path integral simulation techniques within the molecular modelling toolkit [K. Hinsen, J. Comp. Chem. 21, 79 (2000)], 10.1002/(SICI)1096-987X(20000130)21:2<79::AID-JCC1>3.0.CO;2-B, an open-source molecular simulation package.
A path-integral Langevin equation treatment of low-temperature doped helium clusters.
Ing, Christopher; Hinsen, Konrad; Yang, Jing; Zeng, Toby; Li, Hui; Roy, Pierre-Nicholas
2012-06-14
We present an implementation of path integral molecular dynamics for sampling low temperature properties of doped helium clusters using Langevin dynamics. The robustness of the path integral Langevin equation and white-noise Langevin equation [M. Ceriotti, M. Parrinello, T. E. Markland, and D. E. Manolopoulos, J. Chem. Phys. 133, 124104 (2010)] sampling methods are considered for those weakly bound systems with comparison to path integral Monte Carlo (PIMC) in terms of efficiency and accuracy. Using these techniques, convergence studies are performed to confirm the systematic error reduction introduced by increasing the number of discretization steps of the path integral. We comment on the structural and energetic evolution of He(N)-CO(2) clusters from N = 1 to 20. To quantify the importance of both rotations and exchange in our simulations, we present a chemical potential and calculated band origin shifts as a function of cluster size utilizing PIMC sampling that includes these effects. This work also serves to showcase the implementation of path integral simulation techniques within the molecular modelling toolkit [K. Hinsen, J. Comp. Chem. 21, 79 (2000)], an open-source molecular simulation package.
SU(2) Coherent State Path Integrals Labeled by a Full Set of Euler Angles: Basic Formulation
NASA Astrophysics Data System (ADS)
Matsumoto, Masao
2012-11-01
We develop a basic formulation of the spin (SU(2)) coherent state path integrals based not on the conventional highest or lowest weight vectors but on arbitrary fiducial vectors. The coherent states, being defined on a 3-sphere, are specified by a full set of Euler angles. They are generally considered as states without classical analogues. The overcompleteness relation holds for the states, by which we obtain the time evolution of general systems in terms of the path integral representation; the resultant Lagrangian in the action has a monopole-type term à la Balachandran et al. as well as some additional terms, both of which depend on fiducial vectors in a simple way. The process of the discrete path integrals to the continuous ones is clarified. Complex variable forms of the states and path integrals are also obtained. During the course of all steps, we emphasize the analogies and correspondences to the general canonical coherent states and path integrals that we proposed some time ago. In this paper we concentrate on the basic formulation. The physical applications as well as criteria in choosing fiducial vectors for real Lagrangians, in relation to fictitious monopoles and geometric phases, will be treated in subsequent papers separately.
Phase space path integral approach to harmonic oscillator with a time-dependent force constant
NASA Astrophysics Data System (ADS)
Janakiraman, Deepika; Sebastian, K. L.
2015-09-01
The quantum statistical mechanical propagator for a harmonic oscillator with a time-dependent force constant, mω2(t) , has been investigated in the past and was found to have only a formal solution in terms of the solutions of certain ordinary differential equations. Such path integrals are frequently encountered in semiclassical path integral evaluations and having exact analytical expressions for such path integrals is of great interest. In a previous work, we had obtained the exact propagator for motion in an arbitrary time-dependent harmonic potential in the overdamped limit of friction using phase space path integrals in the context of Lévy flights - a result that can be easily extended to Brownian motion. In this paper, we make a connection between the overdamped Brownian motion and the imaginary time propagator of quantum mechanics and thereby get yet another way to evaluate the latter exactly. We find that explicit analytic solution for the quantum statistical mechanical propagator can be written when the time-dependent force constant has the form ω2(t) =λ2(t) - dλ(t)/dt, where λ(t) is any arbitrary function of t and use it to evaluate path integrals which have not been evaluated previously. We also employ this method to arrive at a formal solution of the propagator for both Lévy flights and Brownian subjected to a time-dependent harmonic potential in the underdamped limit of friction.
NASA Astrophysics Data System (ADS)
Halliwell, J. J.; Yearsley, J. M.
2013-06-01
Path integrals appear to offer natural and intuitively appealing methods for defining quantum-mechanical amplitudes for questions involving spacetime regions. For example, the amplitude for entering a spatial region during a given time interval is typically defined by summing over all paths between given initial and final points but restricting them to pass through the region at any time. We argue that there is, however, under very general conditions, a significant complication in such constructions. This is the fact that the concrete implementation of the restrictions on paths over an interval of time corresponds, in an operator language, to sharp monitoring at every moment of time in the given time interval. Such processes suffer from the quantum Zeno effect - the continual monitoring of a quantum system in a Hilbert subspace prevents its state from leaving that subspace. As a consequence, path integral amplitudes defined in this seemingly obvious way have physically and intuitively unreasonable properties and in particular, no sensible classical limit. In this paper we describe this frequently-occurring but little-appreciated phenomenon in some detail, showing clearly the connection with the quantum Zeno effect. We then show that it may be avoided by implementing the restriction on paths in the path integral in a "softer" way. The resulting amplitudes then involve a new coarse graining parameter, which may be taken to be a timescale epsilon, describing the softening of the restrictions on the paths. We argue that the complications arising from the Zeno effect are then negligible as long as epsilon >> 1/E, where E is the energy scale of the incoming state. Our criticisms of path integral constructions largely apply to approaches to quantum theory such as the decoherent histories approach or quantum measure theory, which do not specifically involve measurements. We address some criticisms of our approach by Sokolovksi, concerning the relevance of our results to
Path integral in area tensor Regge calculus and complex connections
NASA Astrophysics Data System (ADS)
Khatsymovsky, V. M.
2006-06-01
Euclidean quantum measure in Regge calculus with independent area tensors is considered using example of the Regge manifold of a simple structure. We go over to integrations along certain contours in the hyperplane of complex connection variables. Discrete connection and curvature on classical solutions of the equations of motion are not, strictly speaking, genuine connection and curvature, but more general quantities and, therefore, these do not appear as arguments of a function to be averaged, but are the integration (dummy) variables. We argue that upon integrating out the latter the resulting measure can be well-defined on physical hypersurface (for the area tensors corresponding to certain edge vectors, i.e. to certain metric) as positive and having exponential cutoff at large areas on condition that we confine ourselves to configurations which do not pass through degenerate metrics.
Travel distance estimation from visual motion by leaky path integration.
Lappe, Markus; Jenkin, Michael; Harris, Laurence R
2007-06-01
Visual motion can be a cue to travel distance when the motion signals are integrated. Distance estimates from visually simulated self-motion are imprecise, however. Previous work in our labs has given conflicting results on the imprecision: experiments by Frenz and Lappe had suggested a general underestimation of travel distance, while results from Redlick, Jenkin and Harris had shown an overestimation of travel distance. Here we describe a collaborative study that resolves the conflict by tracing it to differences in the tasks given to the subjects. With an identical set of subjects and identical visual motion simulation we show that underestimation of travel distance occurs when the task involves a judgment of distance from the starting position, and that overestimation of travel distance occurs when the task requires a judgment of the remaining distance to a particular target position. We present a leaky integrator model that explains both effects with a single mechanism. In this leaky integrator model we introduce the idea that, depending on the task, either the distance from start, or the distance to target is used as a state variable. The state variable is updated during the movement by integration over the space covered by the movement, rather than over time. In this model, travel distance mis-estimation occurs because the integration leaks and because the transformation of visual motion to travel distance involves a gain factor. Mis-estimates in both tasks can be explained with the same leak rate and gain in both conditions. Our results thus suggest that observers do not simply integrate traveled distance and then relate it to the task. Instead, the internally represented variable is either distance from the origin or distance to the goal, whichever is relevant.
PathPPI: an integrated dataset of human pathways and protein-protein interactions.
Tang, HaiLin; Zhong, Fan; Liu, Wei; He, FuChu; Xie, HongWei
2015-06-01
Integration of pathway and protein-protein interaction (PPI) data can provide more information that could lead to new biological insights. PPIs are usually represented by a simple binary model, whereas pathways are represented by more complicated models. We developed a series of rules for transforming protein interactions from pathway to binary model, and the protein interactions from seven pathway databases, including PID, BioCarta, Reactome, NetPath, INOH, SPIKE and KEGG, were transformed based on these rules. These pathway-derived binary protein interactions were integrated with PPIs from other five PPI databases including HPRD, IntAct, BioGRID, MINT and DIP, to develop integrated dataset (named PathPPI). More detailed interaction type and modification information on protein interactions can be preserved in PathPPI than other existing datasets. Comparison analysis results indicate that most of the interaction overlaps values (O AB) among these pathway databases were less than 5%, and these databases must be used conjunctively. The PathPPI data was provided at http://proteomeview.hupo.org.cn/PathPPI/PathPPI.html.
Rad-Path: integrated anatomical pathology and radiology undergraduate tutorials.
Miller, Andrew; Rudland, Joy; Hurrell, Michael; Ali, Anthony
2009-01-01
The anatomical pathology tutorials for the fourth year of our undergraduate medical course at the University of Otago, Christchurch, New Zealand, were re-developed with the aim of promoting more active participation and application of learning by the students in their small group work. Radiology was integrated into half of the pathology tutorials with the objective of enhancing learning of both disciplines. The tutorials were designed to be easy to run for the tutors, who are mostly hospital-based staff. A set of 24 tutor-directed undergraduate anatomical pathology tutorials was re-developed into a case-based, student-centred format. Radiology learning was integrated into 12 tutorials. Student assessment was by way of three short answer examinations spaced throughout the course. Students and tutors completed evaluations of the tutorials. Student evaluations were positive, indicating the tutorials were considered valuable, relevant and a stimulus for thinking. Students and tutors endorsed the benefits of integrated pathology and radiology learning. Assessment results have demonstrated effective learning of pathology and radiology in the tutorials. The tutors found that the tutorials stimulated student engagement and were easy to run. The re-developed anatomical pathology tutorials with the integration of radiology appear to offer a number of benefits for learning of pathology and radiology.
Path integral approach to eikonal and next-to-eikonal exponentiation
NASA Astrophysics Data System (ADS)
Laenen, Eric; Stavenga, Gerben; White, Chris D.
2009-03-01
We approach the issue of exponentiation of soft gauge boson corrections to scattering amplitudes from a path integral point of view. We show that if one represents the amplitude as a first quantized path integral in a mixed coordinate-momentum space representation, a charged particle interacting with a soft gauge field is represented as a Wilson line for a semi-infinite line segment, together with calculable fluctuations. Combining such line segments, we show that exponentiation in an abelian field theory follows immediately from standard path-integral combinatorics. In the non-abelian case, we consider color singlet hard interactions with two outgoing external lines, and obtain a new viewpoint for exponentiation in terms of ``webs'', with a closed form solution for their corresponding color factors. We investigate and clarify the structure of next-to-eikonal corrections.
NASA Astrophysics Data System (ADS)
Han, Muxin; Thiemann, T.
2010-11-01
Path integral formulations for gauge theories must start from the canonical formulation in order to obtain the correct measure. A possible avenue to derive it is to start from the reduced phase space formulation. In this paper we review this rather involved procedure in full generality. Moreover, we demonstrate that the reduced phase space path integral formulation formally agrees with the Dirac's operator constraint quantization and, more specifically, with the master constraint quantization for first-class constraints. For first-class constraints with nontrivial structure functions the equivalence can only be established by passing to Abelian(ized) constraints which is always possible locally in phase space. Generically, the correct configuration space path integral measure deviates from the exponential of the Lagrangian action. The corrections are especially severe if the theory suffers from second-class secondary constraints. In a companion paper we compute these corrections for the Holst and Plebanski formulations of GR on which current spin foam models are based.
Robust path integration in the entorhinal grid cell system with hippocampal feed-back.
Samu, Dávid; Eros, Péter; Ujfalussy, Balázs; Kiss, Tamás
2009-07-01
Animals are able to update their knowledge about their current position solely by integrating the speed and the direction of their movement, which is known as path integration. Recent discoveries suggest that grid cells in the medial entorhinal cortex might perform some of the essential underlying computations of path integration. However, a major concern over path integration is that as the measurement of speed and direction is inaccurate, the representation of the position will become increasingly unreliable. In this paper, we study how allothetic inputs can be used to continually correct the accumulating error in the path integrator system. We set up the model of a mobile agent equipped with the entorhinal representation of idiothetic (grid cell) and allothetic (visual cells) information and simulated its place learning in a virtual environment. Due to competitive learning, a robust hippocampal place code emerges rapidly in the model. At the same time, the hippocampo-entorhinal feed-back connections are modified via Hebbian learning in order to allow hippocampal place cells to influence the attractor dynamics in the entorhinal cortex. We show that the continuous feed-back from the integrated hippocampal place representation is able to stabilize the grid cell code.
NASA Astrophysics Data System (ADS)
Pérez, Alejandro; Tuckerman, Mark E.
2011-08-01
Higher order factorization schemes are developed for path integral molecular dynamics in order to improve the convergence of estimators for physical observables as a function of the Trotter number. The methods are based on the Takahashi-Imada and Susuki decompositions of the Boltzmann operator. The methods introduced improve the averages of the estimators by using the classical forces needed to carry out the dynamics to construct a posteriori weighting factors for standard path integral molecular dynamics. The new approaches are straightforward to implement in existing path integral codes and carry no significant overhead. The Suzuki higher order factorization was also used to improve the end-to-end distance estimator in open path integral molecular dynamics. The new schemes are tested in various model systems, including an ab initio path integral molecular dynamics calculation on the hydrogen molecule and a quantum water model. The proposed algorithms have potential utility for reducing the cost of path integral molecular dynamics calculations of bulk systems.
Pérez, Alejandro; Tuckerman, Mark E
2011-08-14
Higher order factorization schemes are developed for path integral molecular dynamics in order to improve the convergence of estimators for physical observables as a function of the Trotter number. The methods are based on the Takahashi-Imada and Susuki decompositions of the Boltzmann operator. The methods introduced improve the averages of the estimators by using the classical forces needed to carry out the dynamics to construct a posteriori weighting factors for standard path integral molecular dynamics. The new approaches are straightforward to implement in existing path integral codes and carry no significant overhead. The Suzuki higher order factorization was also used to improve the end-to-end distance estimator in open path integral molecular dynamics. The new schemes are tested in various model systems, including an ab initio path integral molecular dynamics calculation on the hydrogen molecule and a quantum water model. The proposed algorithms have potential utility for reducing the cost of path integral molecular dynamics calculations of bulk systems.
PathJam: a new service for integrating biological pathway information.
Glez-Peña, Daniel; Reboiro-Jato, Miguel; Domínguez, Rubén; Gómez-López, Gonzalo; Pisano, David G; Fdez-Riverola, Florentino
2010-10-28
Biological pathways are crucial to much of the scientific research today including the study of specific biological processes related with human diseases. PathJam is a new comprehensive and freely accessible web-server application integrating scattered human pathway annotation from several public sources. The tool has been designed for both (i) being intuitive for wet-lab users providing statistical enrichment analysis of pathway annotations and (ii) giving support to the development of new integrative pathway applications. PathJam’s unique features and advantages include interactive graphs linking pathways and genes of interest, downloadable results in fully compatible formats, GSEA compatible output files and a standardized RESTful API.
Path integral measure, constraints and ghosts for massive gravitons with a cosmological constant
Metaxas, Dimitrios
2009-12-15
For massive gravity in a de Sitter background one encounters problems of stability when the curvature is larger than the graviton mass. I analyze this situation from the path integral point of view and show that it is related to the conformal factor problem of Euclidean quantum (massless) gravity. When a constraint for massive gravity is incorporated and the proper treatment of the path integral measure is taken into account one finds that, for particular choices of the DeWitt metric on the space of metrics (in fact, the same choices as in the massless case), one obtains the opposite bound on the graviton mass.
Ab initio path integral ring polymer molecular dynamics: Vibrational spectra of molecules
NASA Astrophysics Data System (ADS)
Shiga, Motoyuki; Nakayama, Akira
2008-01-01
The path integral ring polymer molecular dynamics method is combined with 'on-the-fly' ab initio electronic structure calculations and applied to vibrational spectra of small molecules, LiH and H 2O, at the room temperature. The results are compared with those of the numerically exact solution and ab initio path integral centroid molecular dynamics calculation. The peak positions in the calculated spectra are found to be reasonable, showing the red-shift due to potential anharmonicity. This unification enables the investigation of real-time quantum dynamics of chemically complex molecular systems on the ab initio Born-Oppenheimer potential energy surface.
A path integral approach to asset-liability management
NASA Astrophysics Data System (ADS)
Decamps, Marc; De Schepper, Ann; Goovaerts, Marc
2006-05-01
Functional integrals constitute a powerful tool in the investigation of financial models. In the recent econophysics literature, this technique was successfully used for the pricing of a number of derivative securities. In the present contribution, we introduce this approach to the field of asset-liability management. We work with a representation of cash flows by means of a two-dimensional delta-function perturbation, in the case of a Brownian model and a geometric Brownian model. We derive closed-form solutions for a finite horizon ALM policy. The results are numerically and graphically illustrated.
Enzymatic Kinetic Isotope Effects from Path-Integral Free Energy Perturbation Theory.
Gao, J
2016-01-01
Path-integral free energy perturbation (PI-FEP) theory is presented to directly determine the ratio of quantum mechanical partition functions of different isotopologs in a single simulation. Furthermore, a double averaging strategy is used to carry out the practical simulation, separating the quantum mechanical path integral exactly into two separate calculations, one corresponding to a classical molecular dynamics simulation of the centroid coordinates, and another involving free-particle path-integral sampling over the classical, centroid positions. An integrated centroid path-integral free energy perturbation and umbrella sampling (PI-FEP/UM, or simply, PI-FEP) method along with bisection sampling was summarized, which provides an accurate and fast convergent method for computing kinetic isotope effects for chemical reactions in solution and in enzymes. The PI-FEP method is illustrated by a number of applications, to highlight the computational precision and accuracy, the rule of geometrical mean in kinetic isotope effects, enhanced nuclear quantum effects in enzyme catalysis, and protein dynamics on temperature dependence of kinetic isotope effects. © 2016 Elsevier Inc. All rights reserved.
A review of path-independent integrals in elastic-plastic fracture mechanics
NASA Technical Reports Server (NTRS)
Kim, Kwang S.; Orange, Thomas W.
1988-01-01
The objective of this paper is to review the path-independent (P-I) integrals in elastic plastic fracture mechanics which have been proposed in recent years to overcome the limitations imposed on the J-integral. The P-I integrals considered are the J-integral by Rice (1968), the thermoelastic P-I integrals by Wilson and Yu (1979) and Gurtin (1979), the J-integral by Blackburn (1972), the J(theta)-integral by Ainsworth et al. (1978), the J-integral by Kishimoto et al. (1980), and the Delta-T(p) and Delta T(p)-asterisk integrals by Alturi et al. (1982). The theoretical foundation of the P-I integrals is examined with an emphasis on whether or not the path independence is maintained in the presence of nonproportional loading and unloading in the plastic regime, thermal gradient, and material inhomogeneities. The simularities, difference, salient features, and limitations of the P-I integrals are discussed. Comments are also made with regard to the physical meaning, the possibility of experimental measurement, and computational aspects.
A review of path-independent integrals in elastic-plastic fracture mechanics, task 4
NASA Technical Reports Server (NTRS)
Kim, K. S.
1985-01-01
The path independent (P-I) integrals in elastic plastic fracture mechanics which have been proposed in recent years to overcome the limitations imposed on the J integral are reviewed. The P-I integrals considered herein are the J integral by Rice, the thermoelastic P-I integrals by Wilson and Yu and by Gurtin, the J* integral by Blackburn, the J sub theta integral by Ainsworth et al., the J integral by Kishimoto et al., and the delta T sub p and delta T* sub p integrals by Atluri et al. The theoretical foundation of these P-I integrals is examined with emphasis on whether or not path independence is maintained in the presence of nonproportional loading and unloading in the plastic regime, thermal gradients, and material inhomogeneities. The similarities, differences, salient features, and limitations of these P-I integrals are discussed. Comments are also made with regard to the physical meaning, the possibility of experimental measurement, and computational aspects.
A review of path-independent integrals in elastic-plastic fracture mechanics
NASA Technical Reports Server (NTRS)
Kim, Kwang S.; Orange, Thomas W.
1988-01-01
The objective of this paper is to review the path-independent (P-I) integrals in elastic plastic fracture mechanics which have been proposed in recent years to overcome the limitations imposed on the J-integral. The P-I integrals considered are the J-integral by Rice (1968), the thermoelastic P-I integrals by Wilson and Yu (1979) and Gurtin (1979), the J-integral by Blackburn (1972), the J(theta)-integral by Ainsworth et al. (1978), the J-integral by Kishimoto et al. (1980), and the Delta-T(p) and Delta T(p)-asterisk integrals by Alturi et al. (1982). The theoretical foundation of the P-I integrals is examined with an emphasis on whether or not the path independence is maintained in the presence of nonproportional loading and unloading in the plastic regime, thermal gradient, and material inhomogeneities. The simularities, difference, salient features, and limitations of the P-I integrals are discussed. Comments are also made with regard to the physical meaning, the possibility of experimental measurement, and computational aspects.
ERIC Educational Resources Information Center
Fraser, J. Scott; Solovey, Andrew D.; Grove, David; Lee, Mo Yee; Greene, Gilbert J.
2012-01-01
A moderate common factors approach is proposed as a synthesis or middle path to integrate common and specific factors in evidence-based approaches to high-risk youth and families. The debate in family therapy between common and specific factors camps is reviewed and followed by suggestions from the literature for synthesis and creative flexibility…
ERIC Educational Resources Information Center
Fraser, J. Scott; Solovey, Andrew D.; Grove, David; Lee, Mo Yee; Greene, Gilbert J.
2012-01-01
A moderate common factors approach is proposed as a synthesis or middle path to integrate common and specific factors in evidence-based approaches to high-risk youth and families. The debate in family therapy between common and specific factors camps is reviewed and followed by suggestions from the literature for synthesis and creative flexibility…
Singular path-independent energy integrals for elastic bodies with thin elastic inclusions
NASA Astrophysics Data System (ADS)
Shcherbakov, V. V.
2016-06-01
An equilibrium problem for a two-dimensional homogeneous linear elastic body containing a thin elastic inclusion and an interfacial crack is considered. The thin inclusion is modeled within the framework of Euler-Bernoulli beam theory. An explicit formula for the first derivative of the energy functional with respect to the crack perturbation along the interface is presented. It is shown that the formulas for the derivative associated with translation and self-similar expansion of the crack are represented as path-independent integrals along smooth contour surrounding one or both crack tips. These path-independent integrals consist of regular and singular terms and are analogs of the well-known Eshelby-Cherepanov-Rice J-integral and Knowles-Sternberg M-integral.
Integrated flight path planning system and flight control system for unmanned helicopters.
Jan, Shau Shiun; Lin, Yu Hsiang
2011-01-01
This paper focuses on the design of an integrated navigation and guidance system for unmanned helicopters. The integrated navigation system comprises two systems: the Flight Path Planning System (FPPS) and the Flight Control System (FCS). The FPPS finds the shortest flight path by the A-Star (A*) algorithm in an adaptive manner for different flight conditions, and the FPPS can add a forbidden zone to stop the unmanned helicopter from crossing over into dangerous areas. In this paper, the FPPS computation time is reduced by the multi-resolution scheme, and the flight path quality is improved by the path smoothing methods. Meanwhile, the FCS includes the fuzzy inference systems (FISs) based on the fuzzy logic. By using expert knowledge and experience to train the FIS, the controller can operate the unmanned helicopter without dynamic models. The integrated system of the FPPS and the FCS is aimed at providing navigation and guidance to the mission destination and it is implemented by coupling the flight simulation software, X-Plane, and the computing software, MATLAB. Simulations are performed and shown in real time three-dimensional animations. Finally, the integrated system is demonstrated to work successfully in controlling the unmanned helicopter to operate in various terrains of a digital elevation model (DEM).
Quantum mechanical path integrals in curved spaces and the type-A trace anomaly
NASA Astrophysics Data System (ADS)
Bastianelli, Fiorenzo; Corradini, Olindo; Vassura, Edoardo
2017-04-01
Path integrals for particles in curved spaces can be used to compute trace anomalies in quantum field theories, and more generally to study properties of quantum fields coupled to gravity in first quantization. While their construction in arbitrary coordinates is well understood, and known to require the use of a regularization scheme, in this article we take up an old proposal of constructing the path integral by using Riemann normal coordinates. The method assumes that curvature effects are taken care of by a scalar effective potential, so that the particle lagrangian is reduced to that of a linear sigma model interacting with the effective potential. After fixing the correct effective potential, we test the construction on spaces of maximal symmetry and use it to compute heat kernel coefficients and type-A trace anomalies for a scalar field in arbitrary dimensions up to d = 12. The results agree with expected ones, which are reproduced with great efficiency and extended to higher orders. We prove explicitly the validity of the simplified path integral on maximally symmetric spaces. This simplified path integral might be of further use in worldline applications, though its application on spaces of arbitrary geometry remains unclear.
Teaching Basic Quantum Mechanics in Secondary School Using Concepts of Feynman Path Integrals Method
ERIC Educational Resources Information Center
Fanaro, Maria de los Angeles; Otero, Maria Rita; Arlego, Marcelo
2012-01-01
This paper discusses the teaching of basic quantum mechanics in high school. Rather than following the usual formalism, our approach is based on Feynman's path integral method. Our presentation makes use of simulation software and avoids sophisticated mathematical formalism. (Contains 3 figures.)
Teaching Basic Quantum Mechanics in Secondary School Using Concepts of Feynman Path Integrals Method
ERIC Educational Resources Information Center
Fanaro, Maria de los Angeles; Otero, Maria Rita; Arlego, Marcelo
2012-01-01
This paper discusses the teaching of basic quantum mechanics in high school. Rather than following the usual formalism, our approach is based on Feynman's path integral method. Our presentation makes use of simulation software and avoids sophisticated mathematical formalism. (Contains 3 figures.)
Coherent-state path integrals in the continuum: The SU(2) case
NASA Astrophysics Data System (ADS)
Kordas, G.; Kalantzis, D.; Karanikas, A. I.
2016-09-01
We define the time-continuous spin coherent-state path integral in a way that is free from inconsistencies. The proposed definition is used to reproduce known exact results. Such a formalism opens new possibilities for applying approximations with improved accuracy and can be proven useful in a great variety of problems where spin Hamiltonians are used.
Path-dependent J-integral evaluations around an elliptical hole for large deformation theory
NASA Astrophysics Data System (ADS)
Unger, David J.
2016-08-01
An exact expression is obtained for a path-dependent J-integral for finite strains of an elliptical hole subject to remote tensile tractions under the Tresca deformation theory for a thin plate composed of non-work hardening material. Possible applications include an analytical resistance curve for the initial stage of crack propagation due to crack tip blunting.
SU(1,1) coherent-state dynamics: A path-integral approach
NASA Astrophysics Data System (ADS)
Gerry, Christopher C.
1989-02-01
We use SU(1,1) coherent-state path integrals to describe the time evolution of systems driven by coherence-preserving Hamiltonians. Such Hamiltonians are composed of linear combinations of the group generators. The method described here is an alternative to the well-known Wei-Norman procedures. Application is made to the degenerate parametric amplifier of quantum optics.
Walters, Peter L; Makri, Nancy
2015-12-17
We employ the quantum-classical path integral methodology to simulate the outer sphere charge-transfer process of the ferrocene-ferrocenium pair in liquid hexane with unprecedented accuracy. Comparison of the simulation results to those obtained by mapping the solvent on an effective harmonic bath demonstrates the accuracy of linear response theory in this system.
A combined explicit-implicit method for high accuracy reaction path integration.
Burger, Steven K; Yang, Weitao
2006-06-14
We present the use of an optimal combined explicit-implicit method for following the reaction path to high accuracy. This is in contrast to most purely implicit reaction path integration algorithms, which are only efficient on stiff ordinary differential equations. The defining equation for the reaction path is considered to be stiff, however, we show here that the reaction path is not uniformly stiff and instead is only stiff near stationary points. The optimal algorithm developed in this work is a combination of explicit and implicit methods with a simple criterion to switch between the two. Using three different chemical reactions, we combine and compare three different integration methods: the implicit trapezoidal method, an explicit stabilized third order algorithm implemented in the code DUMKA3 and the traditional explicit fourth order Runge-Kutta method written in the code RKSUITE. The results for high accuracy show that when the implicit trapezoidal method is combined with either explicit method the number of energy and gradient calculations can potentially be reduced by almost a half compared with integrating either method alone. Finally, to explain the improvements of the combined method we expand on the concepts of stability and stiffness and relate them to the efficiency of integration methods.
Integrated Flight Path Planning System and Flight Control System for Unmanned Helicopters
Jan, Shau Shiun; Lin, Yu Hsiang
2011-01-01
This paper focuses on the design of an integrated navigation and guidance system for unmanned helicopters. The integrated navigation system comprises two systems: the Flight Path Planning System (FPPS) and the Flight Control System (FCS). The FPPS finds the shortest flight path by the A-Star (A*) algorithm in an adaptive manner for different flight conditions, and the FPPS can add a forbidden zone to stop the unmanned helicopter from crossing over into dangerous areas. In this paper, the FPPS computation time is reduced by the multi-resolution scheme, and the flight path quality is improved by the path smoothing methods. Meanwhile, the FCS includes the fuzzy inference systems (FISs) based on the fuzzy logic. By using expert knowledge and experience to train the FIS, the controller can operate the unmanned helicopter without dynamic models. The integrated system of the FPPS and the FCS is aimed at providing navigation and guidance to the mission destination and it is implemented by coupling the flight simulation software, X-Plane, and the computing software, MATLAB. Simulations are performed and shown in real time three-dimensional animations. Finally, the integrated system is demonstrated to work successfully in controlling the unmanned helicopter to operate in various terrains of a digital elevation model (DEM). PMID:22164029
Factors Affecting Technology Integration in K-12 Classrooms: A Path Model
ERIC Educational Resources Information Center
Inan, Fethi A.; Lowther, Deborah L.
2010-01-01
The purpose of this study was to examine the direct and indirect effects of teachers' individual characteristics and perceptions of environmental factors that influence their technology integration in the classroom. A research-based path model was developed to explain causal relationships between these factors and was tested based on data gathered…
Accelerated path integral methods for atomistic simulations at ultra-low temperatures
NASA Astrophysics Data System (ADS)
Uhl, Felix; Marx, Dominik; Ceriotti, Michele
2016-08-01
Path integral methods provide a rigorous and systematically convergent framework to include the quantum mechanical nature of atomic nuclei in the evaluation of the equilibrium properties of molecules, liquids, or solids at finite temperature. Such nuclear quantum effects are often significant for light nuclei already at room temperature, but become crucial at cryogenic temperatures such as those provided by superfluid helium as a solvent. Unfortunately, the cost of converged path integral simulations increases significantly upon lowering the temperature so that the computational burden of simulating matter at the typical superfluid helium temperatures becomes prohibitive. Here we investigate how accelerated path integral techniques based on colored noise generalized Langevin equations, in particular the so-called path integral generalized Langevin equation thermostat (PIGLET) variant, perform in this extreme quantum regime using as an example the quasi-rigid methane molecule and its highly fluxional protonated cousin, CH5+. We show that the PIGLET technique gives a speedup of two orders of magnitude in the evaluation of structural observables and quantum kinetic energy at ultralow temperatures. Moreover, we computed the spatial spread of the quantum nuclei in CH4 to illustrate the limits of using such colored noise thermostats close to the many body quantum ground state.
Applications of Path Integral Langevin Dynamics to Weakly Bound Clusters and Biological Molecules
NASA Astrophysics Data System (ADS)
Ing, Christopher; Hinsen, Conrad; Yang, Jing; Roy, Pierre-Nicholas
2011-06-01
We present the use of path integral molecular dynamics (PIMD) in conjunction with the path integral Langevin equation thermostat for sampling systems that exhibit nuclear quantum effects, notably those at low temperatures or those consisting mainly of hydrogen or helium. To test this approach, the internal energy of doped helium clusters are compared with white-noise Langevin thermostatting and high precision path integral monte carlo (PIMC) simulations. We comment on the structural evolution of these clusters in the absence of rotation and exchange as a function of cluster size. To quantify the importance of both rotation and exchange in our PIMD simulation, we compute band origin shifts for (He)_N-CO_2 as a function of cluster size and compare to previously published experimental and theoretical shifts. A convergence study is presented to confirm the systematic error reduction introduced by increasing path integral beads for our implementation in the Molecular Modelling Toolkit (MMTK) software package. Applications to carbohydrates are explored at biological temperatures by calculating both equilibrium and dynamical properties using the methods presented. M. Ceriotti, M. Parrinello, and D. E. Manolopoulos, J Chem Phys 133, 124104. H. Li, N. Blinov, P.-N. Roy, and R. J. L. Roy, J Chem Phys 130, 144305.
Accelerated path integral methods for atomistic simulations at ultra-low temperatures.
Uhl, Felix; Marx, Dominik; Ceriotti, Michele
2016-08-07
Path integral methods provide a rigorous and systematically convergent framework to include the quantum mechanical nature of atomic nuclei in the evaluation of the equilibrium properties of molecules, liquids, or solids at finite temperature. Such nuclear quantum effects are often significant for light nuclei already at room temperature, but become crucial at cryogenic temperatures such as those provided by superfluid helium as a solvent. Unfortunately, the cost of converged path integral simulations increases significantly upon lowering the temperature so that the computational burden of simulating matter at the typical superfluid helium temperatures becomes prohibitive. Here we investigate how accelerated path integral techniques based on colored noise generalized Langevin equations, in particular the so-called path integral generalized Langevin equation thermostat (PIGLET) variant, perform in this extreme quantum regime using as an example the quasi-rigid methane molecule and its highly fluxional protonated cousin, CH5 (+). We show that the PIGLET technique gives a speedup of two orders of magnitude in the evaluation of structural observables and quantum kinetic energy at ultralow temperatures. Moreover, we computed the spatial spread of the quantum nuclei in CH4 to illustrate the limits of using such colored noise thermostats close to the many body quantum ground state.
Iterative blip-summed path integral for quantum dynamics in strongly dissipative environments.
Makri, Nancy
2017-04-07
The iterative decomposition of the blip-summed path integral [N. Makri, J. Chem. Phys. 141, 134117 (2014)] is described. The starting point is the expression of the reduced density matrix for a quantum system interacting with a harmonic dissipative bath in the form of a forward-backward path sum, where the effects of the bath enter through the Feynman-Vernon influence functional. The path sum is evaluated iteratively in time by propagating an array that stores blip configurations within the memory interval. Convergence with respect to the number of blips and the memory length yields numerically exact results which are free of statistical error. In situations of strongly dissipative, sluggish baths, the algorithm leads to a dramatic reduction of computational effort in comparison with iterative path integral methods that do not implement the blip decomposition. This gain in efficiency arises from (i) the rapid convergence of the blip series and (ii) circumventing the explicit enumeration of between-blip path segments, whose number grows exponentially with the memory length. Application to an asymmetric dissipative two-level system illustrates the rapid convergence of the algorithm even when the bath memory is extremely long.
Iterative blip-summed path integral for quantum dynamics in strongly dissipative environments
NASA Astrophysics Data System (ADS)
Makri, Nancy
2017-04-01
The iterative decomposition of the blip-summed path integral [N. Makri, J. Chem. Phys. 141, 134117 (2014)] is described. The starting point is the expression of the reduced density matrix for a quantum system interacting with a harmonic dissipative bath in the form of a forward-backward path sum, where the effects of the bath enter through the Feynman-Vernon influence functional. The path sum is evaluated iteratively in time by propagating an array that stores blip configurations within the memory interval. Convergence with respect to the number of blips and the memory length yields numerically exact results which are free of statistical error. In situations of strongly dissipative, sluggish baths, the algorithm leads to a dramatic reduction of computational effort in comparison with iterative path integral methods that do not implement the blip decomposition. This gain in efficiency arises from (i) the rapid convergence of the blip series and (ii) circumventing the explicit enumeration of between-blip path segments, whose number grows exponentially with the memory length. Application to an asymmetric dissipative two-level system illustrates the rapid convergence of the algorithm even when the bath memory is extremely long.
PRELIMINARY PROJECT PLAN FOR LANSCE INTEGRATED FLIGHT PATHS 11A, 11B, 12, and 13
D. H. BULTMAN; D. WEINACHT - AIRES CORP.
2000-08-01
This Preliminary Project Plan Summarizes the Technical, Cost, and Schedule baselines for an integrated approach to developing several flight paths at the Manual Lujan Jr. Neutron Scattering Center at the Los Alamos Neutron Science Center. For example, the cost estimate is intended to serve only as a rough order of magnitude assessment of the cost that might be incurred as the flight paths are developed. Further refinement of the requirements and interfaces for each beamline will permit additional refinement and confidence in the accuracy of all three baselines (Technical, Cost, Schedule).
Path integral pricing of Wasabi option in the Black-Scholes model
NASA Astrophysics Data System (ADS)
Cassagnes, Aurelien; Chen, Yu; Ohashi, Hirotada
2014-11-01
In this paper, using path integral techniques, we derive a formula for a propagator arising in the study of occupation time derivatives. Using this result we derive a fair price for the case of the cumulative Parisian option. After confirming the validity of the derived result using Monte Carlo simulation, a new type of heavily path dependent derivative product is investigated. We derive an approximation for our so-called Wasabi option fair price and check the accuracy of our result with a Monte Carlo simulation.
Quantum Mechanics, Path Integrals and Option Pricing:. Reducing the Complexity of Finance
NASA Astrophysics Data System (ADS)
Baaquie, Belal E.; Corianò, Claudio; Srikant, Marakani
2003-04-01
Quantum Finance represents the synthesis of the techniques of quantum theory (quantum mechanics and quantum field theory) to theoretical and applied finance. After a brief overview of the connection between these fields, we illustrate some of the methods of lattice simulations of path integrals for the pricing of options. The ideas are sketched out for simple models, such as the Black-Scholes model, where analytical and numerical results are compared. Application of the method to nonlinear systems is also briefly overviewed. More general models, for exotic or path-dependent options are discussed.
Tcheang, Lili; Bülthoff, Heinrich H; Burgess, Neil
2011-01-18
Our ability to return to the start of a route recently performed in darkness is thought to reflect path integration of motion-related information. Here we provide evidence that motion-related interoceptive representations (proprioceptive, vestibular, and motor efference copy) combine with visual representations to form a single multimodal representation guiding navigation. We used immersive virtual reality to decouple visual input from motion-related interoception by manipulating the rotation or translation gain of the visual projection. First, participants walked an outbound path with both visual and interoceptive input, and returned to the start in darkness, demonstrating the influences of both visual and interoceptive information in a virtual reality environment. Next, participants adapted to visual rotation gains in the virtual environment, and then performed the path integration task entirely in darkness. Our findings were accurately predicted by a quantitative model in which visual and interoceptive inputs combine into a single multimodal representation guiding navigation, and are incompatible with a model of separate visual and interoceptive influences on action (in which path integration in darkness must rely solely on interoceptive representations). Overall, our findings suggest that a combined multimodal representation guides large-scale navigation, consistent with a role for visual imagery or a cognitive map.
Tcheang, Lili; Bülthoff, Heinrich H.; Burgess, Neil
2011-01-01
Our ability to return to the start of a route recently performed in darkness is thought to reflect path integration of motion-related information. Here we provide evidence that motion-related interoceptive representations (proprioceptive, vestibular, and motor efference copy) combine with visual representations to form a single multimodal representation guiding navigation. We used immersive virtual reality to decouple visual input from motion-related interoception by manipulating the rotation or translation gain of the visual projection. First, participants walked an outbound path with both visual and interoceptive input, and returned to the start in darkness, demonstrating the influences of both visual and interoceptive information in a virtual reality environment. Next, participants adapted to visual rotation gains in the virtual environment, and then performed the path integration task entirely in darkness. Our findings were accurately predicted by a quantitative model in which visual and interoceptive inputs combine into a single multimodal representation guiding navigation, and are incompatible with a model of separate visual and interoceptive influences on action (in which path integration in darkness must rely solely on interoceptive representations). Overall, our findings suggest that a combined multimodal representation guides large-scale navigation, consistent with a role for visual imagery or a cognitive map. PMID:21199934
Putz, Mihai V.
2009-01-01
The density matrix theory, the ancestor of density functional theory, provides the immediate framework for Path Integral (PI) development, allowing the canonical density be extended for the many-electronic systems through the density functional closure relationship. Yet, the use of path integral formalism for electronic density prescription presents several advantages: assures the inner quantum mechanical description of the system by parameterized paths; averages the quantum fluctuations; behaves as the propagator for time-space evolution of quantum information; resembles Schrödinger equation; allows quantum statistical description of the system through partition function computing. In this framework, four levels of path integral formalism were presented: the Feynman quantum mechanical, the semiclassical, the Feynman-Kleinert effective classical, and the Fokker-Planck non-equilibrium ones. In each case the density matrix or/and the canonical density were rigorously defined and presented. The practical specializations for quantum free and harmonic motions, for statistical high and low temperature limits, the smearing justification for the Bohr’s quantum stability postulate with the paradigmatic Hydrogen atomic excursion, along the quantum chemical calculation of semiclassical electronegativity and hardness, of chemical action and Mulliken electronegativity, as well as by the Markovian generalizations of Becke-Edgecombe electronic focalization functions – all advocate for the reliability of assuming PI formalism of quantum mechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the (density driving) many-electronic systems. PMID:20087467
Putz, Mihai V
2009-11-10
The density matrix theory, the ancestor of density functional theory, provides the immediate framework for Path Integral (PI) development, allowing the canonical density be extended for the many-electronic systems through the density functional closure relationship. Yet, the use of path integral formalism for electronic density prescription presents several advantages: assures the inner quantum mechanical description of the system by parameterized paths; averages the quantum fluctuations; behaves as the propagator for time-space evolution of quantum information; resembles Schrödinger equation; allows quantum statistical description of the system through partition function computing. In this framework, four levels of path integral formalism were presented: the Feynman quantum mechanical, the semiclassical, the Feynman-Kleinert effective classical, and the Fokker-Planck non-equilibrium ones. In each case the density matrix or/and the canonical density were rigorously defined and presented. The practical specializations for quantum free and harmonic motions, for statistical high and low temperature limits, the smearing justification for the Bohr's quantum stability postulate with the paradigmatic Hydrogen atomic excursion, along the quantum chemical calculation of semiclassical electronegativity and hardness, of chemical action and Mulliken electronegativity, as well as by the Markovian generalizations of Becke-Edgecombe electronic focalization functions - all advocate for the reliability of assuming PI formalism of quantum mechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the (density driving) many-electronic systems.
Walters, Daniel; Stringer, Simon; Rolls, Edmund
2013-01-01
The head direction cell system is capable of accurately updating its current representation of head direction in the absence of visual input. This is known as the path integration of head direction. An important question is how the head direction cell system learns to perform accurate path integration of head direction. In this paper we propose a model of velocity path integration of head direction in which the natural time delay of axonal transmission between a linked continuous attractor network and competitive network acts as a timing mechanism to facilitate the correct speed of path integration. The model effectively learns a "look-up" table for the correct speed of path integration. In simulation, we show that the model is able to successfully learn two different speeds of path integration across two different axonal conduction delays, and without the need to alter any other model parameters. An implication of this model is that, by learning look-up tables for each speed of path integration, the model should exhibit a degree of robustness to damage. In simulations, we show that the speed of path integration is not significantly affected by degrading the network through removing a proportion of the cells that signal rotational velocity.
Walters, Daniel; Stringer, Simon; Rolls, Edmund
2013-01-01
The head direction cell system is capable of accurately updating its current representation of head direction in the absence of visual input. This is known as the path integration of head direction. An important question is how the head direction cell system learns to perform accurate path integration of head direction. In this paper we propose a model of velocity path integration of head direction in which the natural time delay of axonal transmission between a linked continuous attractor network and competitive network acts as a timing mechanism to facilitate the correct speed of path integration. The model effectively learns a “look-up” table for the correct speed of path integration. In simulation, we show that the model is able to successfully learn two different speeds of path integration across two different axonal conduction delays, and without the need to alter any other model parameters. An implication of this model is that, by learning look-up tables for each speed of path integration, the model should exhibit a degree of robustness to damage. In simulations, we show that the speed of path integration is not significantly affected by degrading the network through removing a proportion of the cells that signal rotational velocity. PMID:23526976
Effective descriptions of complex quantum systems: path integrals and operator ordering problems
NASA Astrophysics Data System (ADS)
Eckern, U.; Gruber, M. J.; Schwab, P.
2005-09-01
[Dedicated to Bernhard Mühlschlegel on the occasion ofhis 80th birthday]We study certain aspects of the effective, occasionally called collective, description of complex quantum systems within the framework of the path integral formalism, in which the environment is integrated out. Generalising the standard Feynman-Vernon Caldeira-Leggett model to include a non-linear coupling between particle and environment, and considering a particular spectral density of the coupling, a coordinate-dependent mass (or velocity-dependent potential) is obtained. The related effective quantum theory, which depends on the proper discretisation of the path integral, is derived and discussed. As a result, we find that in general a simple effective low-energy Hamiltonian, in which only the coordinate-dependent mass enters, cannot be formulated. The quantum theory of weakly coupled superconductors and the quantum dynamics of vortices in Josephson junction arrays are physical examples where these considerations, in principle, are of relevance.
Zhang, Sijie; Schönfeld, Fabian; Wiskott, Laurenz; Manahan-Vaughan, Denise
2014-01-01
Effective spatial navigation is enabled by reliable reference cues that derive from sensory information from the external environment, as well as from internal sources such as the vestibular system. The integration of information from these sources enables dead reckoning in the form of path integration. Navigation in the dark is associated with the accumulation of errors in terms of perception of allocentric position and this may relate to error accumulation in path integration. We assessed this by recording from place cells in the dark under circumstances where spatial sensory cues were suppressed. Spatial information content, spatial coherence, place field size, and peak and infield firing rates decreased whereas sparsity increased following exploration in the dark compared to the light. Nonetheless it was observed that place field stability in darkness was sustained by border information in a subset of place cells. To examine the impact of encountering the environment's border on navigation, we analyzed the trajectory and spiking data gathered during navigation in the dark. Our data suggest that although error accumulation in path integration drives place field drift in darkness, under circumstances where border contact is possible, this information is integrated to enable retention of spatial representations.
Zhang, Sijie; Schönfeld, Fabian; Wiskott, Laurenz; Manahan-Vaughan, Denise
2014-01-01
Effective spatial navigation is enabled by reliable reference cues that derive from sensory information from the external environment, as well as from internal sources such as the vestibular system. The integration of information from these sources enables dead reckoning in the form of path integration. Navigation in the dark is associated with the accumulation of errors in terms of perception of allocentric position and this may relate to error accumulation in path integration. We assessed this by recording from place cells in the dark under circumstances where spatial sensory cues were suppressed. Spatial information content, spatial coherence, place field size, and peak and infield firing rates decreased whereas sparsity increased following exploration in the dark compared to the light. Nonetheless it was observed that place field stability in darkness was sustained by border information in a subset of place cells. To examine the impact of encountering the environment’s border on navigation, we analyzed the trajectory and spiking data gathered during navigation in the dark. Our data suggest that although error accumulation in path integration drives place field drift in darkness, under circumstances where border contact is possible, this information is integrated to enable retention of spatial representations. PMID:25009477
Bressloff, Paul C
2015-01-01
We consider applications of path-integral methods to the analysis of a stochastic hybrid model representing a network of synaptically coupled spiking neuronal populations. The state of each local population is described in terms of two stochastic variables, a continuous synaptic variable and a discrete activity variable. The synaptic variables evolve according to piecewise-deterministic dynamics describing, at the population level, synapses driven by spiking activity. The dynamical equations for the synaptic currents are only valid between jumps in spiking activity, and the latter are described by a jump Markov process whose transition rates depend on the synaptic variables. We assume a separation of time scales between fast spiking dynamics with time constant [Formula: see text] and slower synaptic dynamics with time constant τ. This naturally introduces a small positive parameter [Formula: see text], which can be used to develop various asymptotic expansions of the corresponding path-integral representation of the stochastic dynamics. First, we derive a variational principle for maximum-likelihood paths of escape from a metastable state (large deviations in the small noise limit [Formula: see text]). We then show how the path integral provides an efficient method for obtaining a diffusion approximation of the hybrid system for small ϵ. The resulting Langevin equation can be used to analyze the effects of fluctuations within the basin of attraction of a metastable state, that is, ignoring the effects of large deviations. We illustrate this by using the Langevin approximation to analyze the effects of intrinsic noise on pattern formation in a spatially structured hybrid network. In particular, we show how noise enlarges the parameter regime over which patterns occur, in an analogous fashion to PDEs. Finally, we carry out a [Formula: see text]-loop expansion of the path integral, and use this to derive corrections to voltage-based mean-field equations, analogous
2012-01-01
Background Pathway data are important for understanding the relationship between genes, proteins and many other molecules in living organisms. Pathway gene relationships are crucial information for guidance, prediction, reference and assessment in biochemistry, computational biology, and medicine. Many well-established databases--e.g., KEGG, WikiPathways, and BioCyc--are dedicated to collecting pathway data for public access. However, the effectiveness of these databases is hindered by issues such as incompatible data formats, inconsistent molecular representations, inconsistent molecular relationship representations, inconsistent referrals to pathway names, and incomprehensive data from different databases. Results In this paper, we overcome these issues through extraction, normalization and integration of pathway data from several major public databases (KEGG, WikiPathways, BioCyc, etc). We build a database that not only hosts our integrated pathway gene relationship data for public access but also maintains the necessary updates in the long run. This public repository is named IntPath (Integrated Pathway gene relationship database for model organisms and important pathogens). Four organisms--S. cerevisiae, M. tuberculosis H37Rv, H. Sapiens and M. musculus--are included in this version (V2.0) of IntPath. IntPath uses the "full unification" approach to ensure no deletion and no introduced noise in this process. Therefore, IntPath contains much richer pathway-gene and pathway-gene pair relationships and much larger number of non-redundant genes and gene pairs than any of the single-source databases. The gene relationships of each gene (measured by average node degree) per pathway are significantly richer. The gene relationships in each pathway (measured by average number of gene pairs per pathway) are also considerably richer in the integrated pathways. Moderate manual curation are involved to get rid of errors and noises from source data (e.g., the gene ID errors
Functional integration of vertical flight path and speed control using energy principles
NASA Technical Reports Server (NTRS)
Lambregts, A. A.
1984-01-01
A generalized automatic flight control system was developed which integrates all longitudinal flight path and speed control functions previously provided by a pitch autopilot and autothrottle. In this design, a net thrust command is computed based on total energy demand arising from both flight path and speed targets. The elevator command is computed based on the energy distribution error between flight path and speed. The engine control is configured to produce the commanded net thrust. The design incorporates control strategies and hierarchy to deal systematically and effectively with all aircraft operational requirements, control nonlinearities, and performance limits. Consistent decoupled maneuver control is achieved for all modes and flight conditions without outer loop gain schedules, control law submodes, or control function duplication.
The role of spatial memory and frames of reference in the precision of angular path integration.
Arthur, Joeanna C; Philbeck, John W; Kleene, Nicholas J; Chichka, David
2012-09-01
Angular path integration refers to the ability to maintain an estimate of self-location after a rotational displacement by integrating internally-generated (idiothetic) self-motion signals over time. Previous work has found that non-sensory inputs, namely spatial memory, can play a powerful role in angular path integration (Arthur et al., 2007, 2009). Here we investigated the conditions under which spatial memory facilitates angular path integration. We hypothesized that the benefit of spatial memory is particularly likely in spatial updating tasks in which one's self-location estimate is referenced to external space. To test this idea, we administered passive, non-visual body rotations (ranging 40°-140°) about the yaw axis and asked participants to use verbal reports or open-loop manual pointing to indicate the magnitude of the rotation. Prior to some trials, previews of the surrounding environment were given. We found that when participants adopted an egocentric frame of reference, the previously-observed benefit of previews on within-subject response precision was not manifested, regardless of whether remembered spatial frameworks were derived from vision or spatial language. We conclude that the powerful effect of spatial memory is dependent on one's frame of reference during self-motion updating.
Automatic integration of the reaction path using diagonally implicit Runge-Kutta methods.
Burger, Steven K; Yang, Weitao
2006-12-28
The diagonally implicit Runge-Kutta framework is shown to be a general form for constructing stable, efficient steepest descent reaction path integrators, of any order. With this framework tolerance driven, adaptive step-size methods can be constructed by embedding methods to obtain error estimates of each step without additional computational cost. There are many embedded and nonembedded, diagonally implicit Runge-Kutta methods available from the numerical analysis literature and these are reviewed for orders two, three, and four. New embedded methods are also developed which are tailored to the application of reaction path following. All integrators are summarized and compared for three systems: the Muller-Brown [Theor. Chem. Acta 53, 75 (1979)] potential and two gas phase chemical reactions. The results show that many of the methods are capable of integrating efficiently while reliably keeping the error bound within the desired tolerance. This allows the reaction path to be determined through automatic integration by only specifying the desired accuracy and transition state.
Color path integral equation of state of the quark-gluon plasma at nonzero chemical potential
NASA Astrophysics Data System (ADS)
Filinov, V. S.; Bonitz, M.; Ivanov, Yu B.; Ilgenfritz, E.-M.; Fortov, V. E.
2015-04-01
Based on the constituent quasiparticle model of the quark-gluon plasma (QGP), a color quantum path-integral Monte-Carlo (PIMC) method for calculation of the thermodynamic properties of the QGP is developed. We show that the PIMC method can be used for calculations of the equation of state at zero and non-zero baryon chemical potential not only above but also below the QCD critical temperature. Our results agree with lattice QCD calculations based on a Taylor expansion around zero baryon chemical potential. In our approach the QGP partition function is presented in the form of a color path integral with a relativistic measure replacing the Gaussian one traditionally used in the Feynman-Wiener path integrals. A procedure of sampling color variables according to the SU(3) group Haar measure is used for integration over the color variables. We expect that this approach will be useful to predict additional properties of the QGP that are still unaccesible in lattice QCD.
The Role of Spatial Memory and Frames of Reference in the Precision of Angular Path Integration
Arthur, Joeanna C.; Philbeck, John W.; Kleene, Nicholas J.; Chichka, David
2012-01-01
Angular path integration refers to the ability to maintain an estimate of self-location after a rotational displacement by integrating internally-generated (idiothetic) self-motion signals over time. Previous work has found that non-sensory inputs, namely spatial memory, can play a powerful role in angular path integration (Arthur et al., 2007, 2009). Here we investigated the conditions under which spatial memory facilitates angular path integration. We hypothesized that the benefit of spatial memory is particularly likely in spatial updating tasks in which one’s self-location estimate is referenced to external space. To test this idea, we administered passive, nonvisual body rotations (ranging 40° – 140°) about the yaw axis and asked participants to use verbal reports or open-loop manual pointing to indicate the magnitude of the rotation. Prior to some trials, previews of the surrounding environment were given. We found that when participants adopted an egocentric frame of reference, the previously-observed benefit of previews on within-subject response precision was not manifested, regardless of whether remembered spatial frameworks were derived from vision or spatial language. We conclude that the powerful effect of spatial memory is dependent on one’s frame of reference during self-motion updating. PMID:22885073
Blip-summed quantum-classical path integral with cumulative quantum memory.
Makri, Nancy
2016-12-22
The quantum-classical path integral (QCPI) offers a rigorous methodology for simulating quantum mechanical processes in condensed-phase environments treated in full atomistic detail. This paper describes the implementation of QCPI on system-bath models, which are frequently employed in studying the dynamics of reactive processes. The QCPI methodology incorporates all effects associated with stimulated phonon absorption and emission as its crudest limit, thus can (in some regimes) converge faster than influence functional-based path integral methods specifically designed for system-bath Hamiltonians. It is shown that the QCPI phase arising from a harmonic bath can be summed analytically with respect to the discrete bath degrees of freedom and expressed in terms of precomputed influence functional coefficients, avoiding the explicit enumeration of forced oscillator trajectories, whose number grows exponentially with the length of quantum memory. Further, adoption of the blip decomposition (which classifies the system paths based on the time length over which their forward and backward components are not identical) and a cumulative treatment of the QCPI phase between blips allows elimination of the majority of system paths, leading to a dramatic increase in efficiency. The generalization of these acceleration techniques to anharmonic environments is discussed.
The path-independent M Integral around Röthlisberger channels
NASA Astrophysics Data System (ADS)
Meyer, C. R.; Rice, J. R.
2015-12-01
Röthlisberger channels are essential components of subglacial hydrologic systems. Deviations from the Nye creep closure of the ice around a Röthlisberger channel have been long recognized and enhancement factors or a more complex rheology for ice have been suggested as ameliorations to account for channels closing faster than predicted. Here we use the MM integral, a path-independent integral of the equations of continuum mechanics, with a Glen power-law rheology to unify descriptions of creep closure under a variety of stress states surrounding the Röthlisberger channel. The advantage of this approach is that the MM integral around the Röthlisberger channel is equivalent to the integral around the far field. In this way, the creep closure on the channel wall can be determined as a function of the far-field loading, e.g. antiplane shear as well as overburden pressure. We start by analyzing the case of axisymmetric creep closure and we see that the Nye solution is implied by the path-independence of MM integral. We then examine the effects of antiplane shear in several geometries and derive scalings for the creep closure rate based on the MM integral. The results are compared to observations for tunnel closure measurements in a variety of stress states and it is shown that the additional stress components can account for the deviations from the Nye solution. Furthermore, creep closure can be succinctly written in terms of the path-independent MM integral and the variation with applied shear can be found via scalings, which is useful for subglacial hydrology models.
Path-integral and Ornstein-Zernike study of quantum fluid structures on the crystallization line
NASA Astrophysics Data System (ADS)
Sesé, Luis M.
2016-03-01
Liquid neon, liquid para-hydrogen, and the quantum hard-sphere fluid are studied with path integral Monte Carlo simulations and the Ornstein-Zernike pair equation on their respective crystallization lines. The results cover the whole sets of structures in the r-space and the k-space and, for completeness, the internal energies, pressures and isothermal compressibilities. Comparison with experiment is made wherever possible, and the possibilities of establishing k-space criteria for quantum crystallization based on the path-integral centroids are discussed. In this regard, the results show that the centroid structure factor contains two significant parameters related to its main peak features (amplitude and shape) that can be useful to characterize freezing.
Two-scale large deviations for chemical reaction kinetics through second quantization path integral
NASA Astrophysics Data System (ADS)
Li, Tiejun; Lin, Feng
2016-04-01
Motivated by the study of rare events for a typical genetic switching model in systems biology, in this paper we aim to establish the general two-scale large deviations for chemical reaction systems. We build a formal approach to explicitly obtain the large deviation rate functionals for the considered two-scale processes based upon the second quantization path integral technique. We get three important types of large deviation results when the underlying two timescales are in three different regimes. This is realized by singular perturbation analysis to the rate functionals obtained by the path integral. We find that the three regimes possess the same deterministic mean-field limit but completely different chemical Langevin approximations. The obtained results are natural extensions of the classical large volume limit for chemical reactions. We also discuss its implication on the single-molecule Michaelis-Menten kinetics. Our framework and results can be applied to understand general multi-scale systems including diffusion processes.
Anti-de Sitter Space from Optimization of Path Integrals in Conformal Field Theories
NASA Astrophysics Data System (ADS)
Caputa, Pawel; Kundu, Nilay; Miyaji, Masamichi; Takayanagi, Tadashi; Watanabe, Kento
2017-08-01
We introduce a new optimization procedure for Euclidean path integrals, which compute wave functionals in conformal field theories (CFTs). We optimize the background metric in the space on which the path integration is performed. Equivalently, this is interpreted as a position-dependent UV cutoff. For two-dimensional CFT vacua, we find the optimized metric is given by that of a hyperbolic space, and we interpret this as a continuous limit of the conjectured relation between tensor networks and Anti-de Sitter (AdS)/conformal field theory (CFT) correspondence. We confirm our procedure for excited states, the thermofield double state, the Sachdev-Ye-Kitaev model, and discuss its extension to higher-dimensional CFTs. We also show that when applied to reduced density matrices, it reproduces entanglement wedges and holographic entanglement entropy. We suggest that our optimization prescription is analogous to the estimation of computational complexity.
Proton momentum distribution in water: an open path integral molecular dynamics study.
Morrone, Joseph A; Srinivasan, Varadharajan; Sebastiani, Daniel; Car, Roberto
2007-06-21
Recent neutron Compton scattering experiments have detected the proton momentum distribution in water. The theoretical calculation of this property can be carried out via "open" path integral expressions. In this work, present an extension of the staging path integral molecular dynamics method, which is then employed to calculate the proton momentum distributions of water in the solid, liquid, and supercritical phases. We utilize a flexible, single point charge empirical force field to model the system's interactions. The calculated momentum distributions depict both agreement and discrepancies with experiment. The differences may be explained by the deviation of the force field from the true interactions. These distributions provide an abundance of information about the environment and interactions surrounding the proton.
van Zon, Ramses; Hernández de la Peña, Lisandro; Peslherbe, Gilles H; Schofield, Jeremy
2008-10-01
Nonequilibrium path-integral methods for computing quantum free-energy differences are applied to a quantum particle trapped in a harmonic well of uniformly changing strength with the purpose of establishing the convergence properties of the work distribution and free energy as the number of degrees of freedom M in the regularized path integrals goes to infinity. The work distribution is found to converge when M tends to infinity regardless of the switching speed, leading to finite results for the free-energy difference when the Jarzynski nonequilibrium work relation or the Crooks fluctuation relation are used. The nature of the convergence depends on the regularization method. For the Fourier method, the convergence of the free-energy difference and work distribution go as 1/M , while both quantities converge as 1/M(2) when the bead regularization procedure is used. The implications of these results to more general systems are discussed.
Moran, B.; Kulkarni, S.S.; Reeves, H.W.
2007-01-01
A path-independent (conservation) integral is developed for the characterization of solute concentration and flux in a biofilm in the vicinity of a detachment or other flux limiting boundary condition. Steady state conditions of solute diffusion are considered and biofilm kinetics are described by an uptake term which can be expressed in terms of a potential (Michaelis-Menten kinetics). An asymptotic solution for solute concentration at the tip of the detachment is obtained and shown to be analogous to that of antiplane crack problems in linear elasticity. It is shown that the amplitude of the asymptotic solution can be calculated by evaluating a path-independent integral. The special case of a semi-infinite detachment in an infinite strip is considered and the amplitude of the asymptotic field is related to the boundary conditions and problem parameters in closed form for zeroth and first order kinetics and numerically for Michaelis-Menten kinetics. ?? Springer Science+Business Media, Inc. 2007.
Path-integral and Ornstein-Zernike study of quantum fluid structures on the crystallization line.
Sesé, Luis M
2016-03-07
Liquid neon, liquid para-hydrogen, and the quantum hard-sphere fluid are studied with path integral Monte Carlo simulations and the Ornstein-Zernike pair equation on their respective crystallization lines. The results cover the whole sets of structures in the r-space and the k-space and, for completeness, the internal energies, pressures and isothermal compressibilities. Comparison with experiment is made wherever possible, and the possibilities of establishing k-space criteria for quantum crystallization based on the path-integral centroids are discussed. In this regard, the results show that the centroid structure factor contains two significant parameters related to its main peak features (amplitude and shape) that can be useful to characterize freezing.
From path integrals to tensor networks for the AdS /CFT correspondence
NASA Astrophysics Data System (ADS)
Miyaji, Masamichi; Takayanagi, Tadashi; Watanabe, Kento
2017-03-01
In this paper, we discuss tensor network descriptions of AdS /CFT from two different viewpoints. First, we start with a Euclidean path-integral computation of ground state wave functions with a UV cutoff. We consider its efficient optimization by making its UV cutoff position dependent and define a quantum state at each length scale. We conjecture that this path integral corresponds to a time slice of anti-de Sitter (AdS) spacetime. Next, we derive a flow of quantum states by rewriting the action of Killing vectors of AdS3 in terms of the dual two-dimensional conformal field theory (CFT). Both approaches support a correspondence between the hyperbolic time slice H2 in AdS3 and a version of continuous multiscale entanglement renormalization ansatz. We also give a heuristic argument about why we can expect a sub-AdS scale bulk locality for holographic CFTs.
Path-integral action of a particle in the noncommutative phase-space
NASA Astrophysics Data System (ADS)
Gangopadhyay, Sunandan; Halder, Aslam
2017-01-01
In this paper we construct a path integral formulation of quantum mechanics on noncommutative phase-space. We first map the system to an equivalent system on the noncommutative plane. Then by applying the formalism of representing a quantum system in the space of Hilbert-Schmidt operators acting on noncommutative configuration space, the path integral action of a particle is derived. It is observed that the action has a similar form to that of a particle in a magnetic field in the noncommutative plane. From this action the energy spectrum is obtained for the free particle and the harmonic-oscillator potential. We also show that the nonlocal nature (in time) of the action yields a second-class constrained system from which the noncommutative Heisenberg algebra can be recovered.
Path integral approach to the pricing of timer options with the Duru-Kleinert time transformation.
Liang, L Z J; Lemmens, D; Tempere, J
2011-05-01
In this paper, a time substitution as used by Duru and Kleinert in their treatment of the hydrogen atom with path integrals is performed to price timer options under stochastic volatility models. We present general pricing formulas for both the perpetual timer call options and the finite time-horizon timer call options. These general results allow us to find closed-form pricing formulas for both the perpetual and the finite time-horizon timer options under the 3/2 stochastic volatility model as well as under the Heston stochastic volatility model. For the treatment of timer options under the 3/2 model we will rely on the path integral for the Morse potential, with the Heston model we will rely on the Kratzer potential. © 2011 American Physical Society
Efficient algorithms for semiclassical instanton calculations based on discretized path integrals
Kawatsu, Tsutomu E-mail: smiura@mail.kanazawa-u.ac.jp; Miura, Shinichi E-mail: smiura@mail.kanazawa-u.ac.jp
2014-07-14
Path integral instanton method is a promising way to calculate the tunneling splitting of energies for degenerated two state systems. In order to calculate the tunneling splitting, we need to take the zero temperature limit, or the limit of infinite imaginary time duration. In the method developed by Richardson and Althorpe [J. Chem. Phys. 134, 054109 (2011)], the limit is simply replaced by the sufficiently long imaginary time. In the present study, we have developed a new formula of the tunneling splitting based on the discretized path integrals to take the limit analytically. We have applied our new formula to model systems, and found that this approach can significantly reduce the computational cost and gain the numerical accuracy. We then developed the method combined with the electronic structure calculations to obtain the accurate interatomic potential on the fly. We present an application of our ab initio instanton method to the ammonia umbrella flip motion.
Path integral investigation of the electronic spectra of He-tetracene clusters
NASA Astrophysics Data System (ADS)
Whitley, Heather D.; Whaley, K. Birgitta
2008-03-01
Planar aromatic molecules (PAMs) are nanoscale precursors to bulk graphite. Their electronic spectra have been extensively studied in ^4He nanodroplets and show a number of unusual spectroscopic features. We have conducted many-body quantum simulations of tetracene in He nanodroplets to probe the 1.1 cm-1 spectral splitting of the electronic origin seen for this PAM. We calculate spectral shifts and He density profiles via path integral quantum Monte Carlo simulations. The spectral splitting is examined using a path integral correlation function approach to determine the lowest-lying vibrational excitation frequencies for small HeN-tetracene clusters. Simulations in the S1 state of tetracene utilize a semi-empirical perturbative interaction potential for a He atom with a PAM. Results for the splitting of the electronic origin and the spectral shifts are in good agreement with experiment. Prepared by LLNL under Contract DE-AC52-07NA27344.
Path integral methods for the dynamics of stochastic and disordered systems
NASA Astrophysics Data System (ADS)
Hertz, John A.; Roudi, Yasser; Sollich, Peter
2017-01-01
We review some of the techniques used to study the dynamics of disordered systems subject to both quenched and fast (thermal) noise. Starting from the Martin-Siggia-Rose/Janssen-De Dominicis-Peliti path integral formalism for a single variable stochastic dynamics, we provide a pedagogical survey of the perturbative, i.e. diagrammatic, approach to dynamics and how this formalism can be used for studying soft spin models. We review the supersymmetric formulation of the Langevin dynamics of these models and discuss the physical implications of the supersymmetry. We also describe the key steps involved in studying the disorder-averaged dynamics. Finally, we discuss the path integral approach for the case of hard Ising spins and review some recent developments in the dynamics of such kinetic Ising models.
Proton momentum distributions in water: A path integral molecular dynamics study
NASA Astrophysics Data System (ADS)
Srinivasan, Varadharajan; Morrone, Joseph A.; Sebastiani, Daniel; Car, Roberto
2007-03-01
Recent neutron Compton scattering experiments have detected the proton momentum distributions of water. This density in momentum space is a quantum mechanical property of the proton, due to the confining anharmonic potential from covalent and hydrogen bonds. The theoretical calculation of this property can be carried out via ``open'' path integral expressions. In this work, we present an extension of the staging path integral molecular dynamics method, which is then employed to calculate the proton momentum distributions of water in the solid, liquid, and supercritical phases. We utilize the SPC/F2 empirical force field to model the system's interactions. The calculated momentum distributions depict both agreement and discrepancies with experiment. The differences may be explained by the deviation of the force field from the true interactions. These distributions provide an abundance of information about the environment and interactions surrounding the proton.
Proton momentum distribution in water: an open path integral molecular dynamics study
NASA Astrophysics Data System (ADS)
Morrone, Joseph A.; Srinivasan, Varadharajan; Sebastiani, Daniel; Car, Roberto
2007-06-01
Recent neutron Compton scattering experiments have detected the proton momentum distribution in water. The theoretical calculation of this property can be carried out via "open" path integral expressions. In this work, present an extension of the staging path integral molecular dynamics method, which is then employed to calculate the proton momentum distributions of water in the solid, liquid, and supercritical phases. We utilize a flexible, single point charge empirical force field to model the system's interactions. The calculated momentum distributions depict both agreement and discrepancies with experiment. The differences may be explained by the deviation of the force field from the true interactions. These distributions provide an abundance of information about the environment and interactions surrounding the proton.
Simulations of one- and two-electron systems by Bead-Fourier path integral molecular dynamics
NASA Astrophysics Data System (ADS)
Ivanov, Sergei D.; Lyubartsev, Alexander P.
2005-07-01
The Bead-Fourier path integral molecular dynamics technique introduced earlier [S. D. Ivanov, A. P. Lyubartsev, and A. Laaksonen, Phys. Rev. E 67 066710 (2003)] is applied for simulation of electrons in the simplest molecules: molecular hydrogen, helium atom, and their ions. Special attention is paid to the correct description of electrons in the core region of a nucleus. In an attempt to smooth the Coulomb potential at small distances, a recipe is suggested. The simulation results are in excellent agreement with the analytical solution for the "harmonic helium atom", as well as with the vibrational potential of the H2 molecule and He ionization energies. It is demonstrated, that the Bead-Fourier path integral molecular dynamics technique is able to provide the accuracy required for the description of electron structure and chemical bonds in cases when electron exchange effects need not be taken into account.
Ab Initio Path Integral Molecular Dynamics Simulation of Hydrogen in Silicon
NASA Astrophysics Data System (ADS)
Probert, M. I. J.; Glover, M. J.
2006-05-01
We report results of a first-principles theoretical study of an isolated neutral hydrogen atom in crystalline silicon. Spin-polarised density functional theory is used to treat the electrons, and the path-integral molecular dynamics method is used to describe the quantum properties of the nucleus at finite temperature. This is necessary as the hydrogen atom has sufficiently low mass that it exhibits significant nuclear quantum delocalisation and zero-point motion even at room temperature. Unlike post-hoc treatments, such as calculating a static potential energy surface, the path-integral treatment enables such effects to be included "on-the-fly". This is found to be significant, as a coupling is found between the structure of the host silicon lattice and the quantum delocalisation of the hydrogen defect.
A unified scheme for ab initio molecular orbital theory and path integral molecular dynamics
NASA Astrophysics Data System (ADS)
Shiga, Motoyuki; Tachikawa, Masanori; Miura, Shinichi
2001-11-01
We present a general approach for accurate calculation of chemical substances which treats both nuclei and electrons quantum mechanically, adopting ab initio molecular orbital theory for the electronic structure and path integral molecular dynamics for the nuclei. The present approach enables the evaluation of physical quantities dependent on the nuclear configuration as well as the electronic structure, within the framework of Born-Oppenheimer adiabatic approximation. As an application, we give the path integral formulation of electric response properties—dipole moment and polarizability, which characterize the changes both in electronic structure and nuclear configuration at a given temperature when uniform electrostatic field is present. We also demonstrate the calculation of a water molecule using the present approach and the result of temperature and isotope effects is discussed.
NASA Technical Reports Server (NTRS)
Yu, Jirong; Petros, Mulugeta; Reithmaier, Karl; Bai, Yingxin; Trieu, Bo C.; Refaat, Tamer F.; Kavaya, Michael J.; Singh, Upendra N.
2012-01-01
A 2-micron pulsed, Integrated Path Differential Absorption (IPDA) lidar instrument for ground and airborne atmospheric CO2 concentration measurements via direct detection method is being developed at NASA Langley Research Center. This instrument will provide an alternate approach to measure atmospheric CO2 concentrations with significant advantages. A high energy pulsed approach provides high-precision measurement capability by having high signal-to-noise level and unambiguously eliminates the contamination from aerosols and clouds that can bias the IPDA measurement.
Path integral solution for a deformed radial Rosen-Morse potential
NASA Astrophysics Data System (ADS)
Kadja, A.; Benamira, F.; Guechi, L.
2017-03-01
An exact path integral treatment of a particle in a deformed radial Rosen-Morse potential is presented. For this problem with the Dirichlet boundary conditions, the Green's function is constructed in a closed form by adding to Vq(r) a δ-function perturbation and making its strength infinitely repulsive. A transcendental equation for the energy levels E_{nr} and the wave functions of the bound states can then be deduced.
Path integral formalism for the spectral line shape in plasmas: Lyman-{alpha} with fine structure
Bedida, N.; Meftah, M. T.; Boland, D.; Stamm, R.
2008-10-22
We examine in this work the expression of the dipolar autocorrelation function for an emitter in the plasma using the path integrals formalism. The results for Lyman alpha lines with fine structure are retrieved in a compact formula. The expression of the dipolar autocorrelation function takes into account the ions dynamics and the fine structure effects. The electron's effect is represented by the impact operator {phi}{sub e} in the final formula.
NASA Astrophysics Data System (ADS)
Gorbenko, Anna; Popov, Vladimir
2017-07-01
Different planning problems for robotic remote laser welding are of considerable interest. In this paper, we consider the problem of integrated task sequencing and path planning for robotic remote laser welding. We propose an efficient approach to solve the problem. In particular, we consider an explicit reduction from the decision version of the problem to the satisfiability problem. We present the results of computational experiments for different satisfiability algorithms.
Path-integral simulations of zero-point effects for implanted muons in benzene
NASA Astrophysics Data System (ADS)
Valladares, R. M.; Fisher, A. J.; Hayes, W.
1995-08-01
We describe a simulation method which is capable of treating the quantum fluctuations of an implanted muon and the electronic structure of the system simultaneously. The partition function for the muon is evaluated using a discretized imaginary-time path-integral technique, using electronic energies and forces evaluated from a semi-empirical quantum chemical treatment of the electronic structure. An application to the cyclohexadienyl radical (C 6H 7) and its muonated analogue (C 6H 6Mu) is presented.
Equation of State of Strongly Coupled Quark-Gluon Plasma - Path Integral Monte Carlo Results
NASA Astrophysics Data System (ADS)
Filinov, V. S.; Bonitz, M.; Ivanov, Y. B.; Skokov, V. V.; Levashov, P. R.; Fortov, V. E.
2009-09-01
A strongly coupled plasma of quark and gluon quasiparticles at temperatures from $ 1.1 T_c$ to $3 T_c$ is studied by path integral Monte Carlo simulations. This method extends previous classical nonrelativistic simulations based on a color Coulomb interaction to the quantum regime. We present the equation of state and find good agreement with lattice results. Further, pair distribution functions and color correlation functions are computed indicating strong correlations and liquid-like behavior.
Path integrals, differential renormalization-group, and stochastic systems near criticality
NASA Technical Reports Server (NTRS)
Chang, Tom
1992-01-01
It is demonstrated, using the techniques of path integrals and renormalization-group, that nonlinear stochastic systems near criticality (including self-organized criticality) generally exhibit low-dimensional behavior. The symmetry which characterizes a particular criticality can be broken by the appearance of relevant scaling fields. A connection is made between the fractal dimensions of finite-dimensional chaotic systems and the anomalous dimensions in stochastic systems near criticality. The effect of additional random noise on stochastic systems is also delineated.
Dornheim, Tobias; Schoof, Tim; Groth, Simon; Filinov, Alexey; Bonitz, Michael
2015-11-28
The uniform electron gas (UEG) at finite temperature is of high current interest due to its key relevance for many applications including dense plasmas and laser excited solids. In particular, density functional theory heavily relies on accurate thermodynamic data for the UEG. Until recently, the only existing first-principle results had been obtained for N = 33 electrons with restricted path integral Monte Carlo (RPIMC), for low to moderate density, rs=r¯/aB≳1. These data have been complemented by configuration path integral Monte Carlo (CPIMC) simulations for rs ≤ 1 that substantially deviate from RPIMC towards smaller rs and low temperature. In this work, we present results from an independent third method-the recently developed permutation blocking path integral Monte Carlo (PB-PIMC) approach [T. Dornheim et al., New J. Phys. 17, 073017 (2015)] which we extend to the UEG. Interestingly, PB-PIMC allows us to perform simulations over the entire density range down to half the Fermi temperature (θ = kBT/EF = 0.5) and, therefore, to compare our results to both aforementioned methods. While we find excellent agreement with CPIMC, where results are available, we observe deviations from RPIMC that are beyond the statistical errors and increase with density.
Phase space path-integral formulation of the above-threshold ionization
NASA Astrophysics Data System (ADS)
Milošević, D. B.
2013-04-01
Atoms and molecules submitted to a strong laser field can emit electrons of high energies in the above-threshold ionization (ATI) process. This process finds a highly intuitive and also quantitative explanation in terms of Feynman's path integral and the concept of quantum orbits [P. Salières et al., Science 292, 902 (2001)], 10.1126/science.108836. However, the connection with the Feynman path-integral formalism is explained only by intuition and analogy and within the so-called strong-field approximation (SFA). Using the phase space path-integral formalism we have obtained an exact result for the momentum-space matrix element of the total time-evolution operator. Applying this result to the ATI we show that the SFA and the so-called improved SFA are, respectively, the zeroth- and the first-order terms of the expansion in powers of the laser-free effective interaction of the electron with the rest of the atom (molecule). We have also presented the second-order term of this expansion which is responsible for the ATI with double scattering of the ionized electron.
Integrating cell on chip—Novel waveguide platform employing ultra-long optical paths
NASA Astrophysics Data System (ADS)
Fohrmann, Lena Simone; Sommer, Gerrit; Pitruzzello, Giampaolo; Krauss, Thomas F.; Petrov, Alexander Yu.; Eich, Manfred
2017-09-01
Optical waveguides are the most fundamental building blocks of integrated optical circuits. They are extremely well understood, yet there is still room for surprises. Here, we introduce a novel 2D waveguide platform which affords a strong interaction of the evanescent tail of a guided optical wave with an external medium while only employing a very small geometrical footprint. The key feature of the platform is its ability to integrate the ultra-long path lengths by combining low propagation losses in a silicon slab with multiple reflections of the guided wave from photonic crystal (PhC) mirrors. With a reflectivity of 99.1% of our tailored PhC-mirrors, we achieve interaction paths of 25 cm within an area of less than 10 mm2. This corresponds to 0.17 dB/cm effective propagation which is much lower than the state-of-the-art loss of approximately 1 dB/cm of single mode silicon channel waveguides. In contrast to conventional waveguides, our 2D-approach leads to a decay of the guided wave power only inversely proportional to the optical path length. This entirely different characteristic is the major advantage of the 2D integrating cell waveguide platform over the conventional channel waveguide concepts that obey the Beer-Lambert law.
Calculation of heat capacities of light and heavy water by path-integral molecular dynamics
NASA Astrophysics Data System (ADS)
Shiga, Motoyuki; Shinoda, Wataru
2005-10-01
As an application of atomistic simulation methods to heat capacities, path-integral molecular dynamics has been used to calculate the constant-volume heat capacities of light and heavy water in the gas, liquid, and solid phases. While the classical simulation based on conventional molecular dynamics has estimated the heat capacities too high, the quantum simulation based on path-integral molecular dynamics has given reasonable results based on the simple point-charge/flexible potential model. The calculated heat capacities (divided by the Boltzmann constant) in the quantum simulation are 3.1 in the vapor H2O at 300 K, 6.9 in the liquid H2O at 300 K, and 4.1 in the ice IhH2O at 250 K, respectively, which are comparable to the experimental data of 3.04, 8.9, and 4.1, respectively. The quantum simulation also reproduces the isotope effect. The heat capacity in the liquid D2O has been calculated to be 10% higher than that of H2O, while it is 13% higher in the experiment. The results demonstrate that the path-integral simulation is a promising approach to quantitatively evaluate the heat capacities for molecular systems, taking account of quantum-mechanical vibrations as well as strongly anharmonic motions.
i-PI: A Python interface for ab initio path integral molecular dynamics simulations
NASA Astrophysics Data System (ADS)
Ceriotti, Michele; More, Joshua; Manolopoulos, David E.
2014-03-01
Recent developments in path integral methodology have significantly reduced the computational expense of including quantum mechanical effects in the nuclear motion in ab initio molecular dynamics simulations. However, the implementation of these developments requires a considerable programming effort, which has hindered their adoption. Here we describe i-PI, an interface written in Python that has been designed to minimise the effort required to bring state-of-the-art path integral techniques to an electronic structure program. While it is best suited to first principles calculations and path integral molecular dynamics, i-PI can also be used to perform classical molecular dynamics simulations, and can just as easily be interfaced with an empirical forcefield code. To give just one example of the many potential applications of the interface, we use it in conjunction with the CP2K electronic structure package to showcase the importance of nuclear quantum effects in high-pressure water. Catalogue identifier: AERN_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AERN_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 No. of lines in distributed program, including test data, etc.: 138626 No. of bytes in distributed program, including test data, etc.: 3128618 Distribution format: tar.gz Programming language: Python. Computer: Multiple architectures. Operating system: Linux, Mac OSX, Windows. RAM: Less than 256 Mb Classification: 7.7. External routines: NumPy Nature of problem: Bringing the latest developments in the modelling of nuclear quantum effects with path integral molecular dynamics to ab initio electronic structure programs with minimal implementational effort. Solution method: State-of-the-art path integral molecular dynamics techniques are implemented in a Python interface. Any electronic structure code can be patched to receive the atomic
NASA Astrophysics Data System (ADS)
Yu, Pengfei; Wang, Hailong; Chen, Jianyong; Shen, Shengping
2017-07-01
In this study, the conservation laws οf dissipative mechanical-diffusion-electrochemical reaction system are systematically obtained based on Noether's theorem. According to linear, irreversible thermodynamics, dissipative phenomena can be described by an irreversible force and an irreversible flow. Additionally, the Lagrange function, L and the generalized Hamilton least-action principle are proposed to be used to obtain the conservation integrals. A group of these integrals, including the J-, M-, and L-integrals, can be then obtained using the classical Noether approach for dissipative processes. The relation between the J-integral and the energy release rate is illustrated. The path-independence of the J-integral is then proven. The J-integral, derived based on Noether's theorem, is a line integral, contrary to the propositions of existing published works that describe it both as a line and an area integral. Herein, we prove that the outcomes are identical, and identify the physical meaning of the area integral, a concept that was not explained previously. To show that the J-integral can dominate the distribution of the corresponding field quantities, an example of a partial, stress-diffusion coupling process is disscussed.
NASA Astrophysics Data System (ADS)
Imaoka, Haruna; Kinugawa, Kenichi
2017-03-01
Thermal conductivity, shear viscosity, and bulk viscosity of normal liquid 4He at 1.7-4.0 K are calculated using path integral centroid molecular dynamics (CMD) simulations. The calculated thermal conductivity and shear viscosity above lambda transition temperature are on the same order of magnitude as experimental values, while the agreement of shear viscosity is better. Above 2.3 K the CMD well reproduces the temperature dependences of isochoric shear viscosity and of the time integral of the energy current and off-diagonal stress tensor correlation functions. The calculated bulk viscosity, not known in experiments, is several times larger than shear viscosity.
Treatment of the hydrogen atom in an electric field by the path-integral formalism
Chetouani, L.; Hammann, T.F.
1986-12-01
The Feynman path-integral method is applied to solve the problem of a H atom in an electric field. In accordance with the midpoint philosophy, the propagators are symmetrized in every time interval and, via several transformations, one of which is the Langer modification, the Green's function is calculated in parabolic coordinates, decomposed into partial propagators, and expressed in terms of two one-dimensional Green's functions. The perturbation method being no more valid for high excited levels, the spectrum is given, according to the WKB method, as a solution of a system of two elliptic integral equations. The exact spectrum of the H atom is obtained for a zero electric field.
NASA Astrophysics Data System (ADS)
Han, Muxin
2010-12-01
This paper serves as a continuation for the discussion in Engle et al (2010, Class. Quantum Grav. 27 245014). We analyze the invariance properties of the gravity path-integral measure derived from canonical framework and discuss which path-integral formula may be employed in the concrete computation e.g. constructing a spin-foam model, so that the final model can be interpreted as a physical inner product in the canonical theory. This paper is divided into two parts, the first part is concerning the gauge invariance of the canonical path-integral measure for gravity from the reduced phase space quantization. We show that the path-integral measure is invariant under all the gauge transformations generated by all the constraints. These gauge transformations are the local symmetries of the gravity action, which is implemented without anomaly at the quantum level by the invariant path-integral measure. However, these gauge transformations coincide with the spacetime diffeomorphisms only when the equations of motion are imposed. But the path-integral measure is not invariant under spacetime diffeomorphisms, i.e. the local symmetry of spacetime diffeomorphisms become anomalous in the reduced phase space path-integral quantization. In the second part, we present a path-integral formula, which formally solves all the quantum constraint equations of gravity, and further results in a rigging map in the sense of refined algebraic quantization (RAQ). Then we give a formal path-integral expression of the physical inner product in loop quantum gravity (LQG). This path-integral expression is simpler than the one from reduced phase space quantization, since all the gauge-fixing conditions are removed except the time gauge. The resulting path-integral measure is different from the product Lebesgue measure up to a local measure factor containing both the spacetime volume element and the spatial volume element. This formal path-integral expression of the physical inner product can be
Accurate path integration in continuous attractor network models of grid cells.
Burak, Yoram; Fiete, Ila R
2009-02-01
Grid cells in the rat entorhinal cortex display strikingly regular firing responses to the animal's position in 2-D space and have been hypothesized to form the neural substrate for dead-reckoning. However, errors accumulate rapidly when velocity inputs are integrated in existing models of grid cell activity. To produce grid-cell-like responses, these models would require frequent resets triggered by external sensory cues. Such inadequacies, shared by various models, cast doubt on the dead-reckoning potential of the grid cell system. Here we focus on the question of accurate path integration, specifically in continuous attractor models of grid cell activity. We show, in contrast to previous models, that continuous attractor models can generate regular triangular grid responses, based on inputs that encode only the rat's velocity and heading direction. We consider the role of the network boundary in the integration performance of the network and show that both periodic and aperiodic networks are capable of accurate path integration, despite important differences in their attractor manifolds. We quantify the rate at which errors in the velocity integration accumulate as a function of network size and intrinsic noise within the network. With a plausible range of parameters and the inclusion of spike variability, our model networks can accurately integrate velocity inputs over a maximum of approximately 10-100 meters and approximately 1-10 minutes. These findings form a proof-of-concept that continuous attractor dynamics may underlie velocity integration in the dorsolateral medial entorhinal cortex. The simulations also generate pertinent upper bounds on the accuracy of integration that may be achieved by continuous attractor dynamics in the grid cell network. We suggest experiments to test the continuous attractor model and differentiate it from models in which single cells establish their responses independently of each other.
Accurate Path Integration in Continuous Attractor Network Models of Grid Cells
Burak, Yoram; Fiete, Ila R.
2009-01-01
Grid cells in the rat entorhinal cortex display strikingly regular firing responses to the animal's position in 2-D space and have been hypothesized to form the neural substrate for dead-reckoning. However, errors accumulate rapidly when velocity inputs are integrated in existing models of grid cell activity. To produce grid-cell-like responses, these models would require frequent resets triggered by external sensory cues. Such inadequacies, shared by various models, cast doubt on the dead-reckoning potential of the grid cell system. Here we focus on the question of accurate path integration, specifically in continuous attractor models of grid cell activity. We show, in contrast to previous models, that continuous attractor models can generate regular triangular grid responses, based on inputs that encode only the rat's velocity and heading direction. We consider the role of the network boundary in the integration performance of the network and show that both periodic and aperiodic networks are capable of accurate path integration, despite important differences in their attractor manifolds. We quantify the rate at which errors in the velocity integration accumulate as a function of network size and intrinsic noise within the network. With a plausible range of parameters and the inclusion of spike variability, our model networks can accurately integrate velocity inputs over a maximum of ∼10–100 meters and ∼1–10 minutes. These findings form a proof-of-concept that continuous attractor dynamics may underlie velocity integration in the dorsolateral medial entorhinal cortex. The simulations also generate pertinent upper bounds on the accuracy of integration that may be achieved by continuous attractor dynamics in the grid cell network. We suggest experiments to test the continuous attractor model and differentiate it from models in which single cells establish their responses independently of each other. PMID:19229307
Yang, Sandy; Yamamoto, Takeshi; Miller, William H.
2005-11-28
The quantum instanton approximation is a type of quantum transition state theory that calculates the chemical reaction rate using the reactive flux correlation function and its low order derivatives at time zero. Here we present several path-integral estimators for the latter quantities, which characterize the initial decay profile of the flux correlation function. As with the internal energy or heat capacity calculation, different estimators yield different variances (and therefore different convergence properties) in a Monte Carlo calculation. Here we obtain a virial(-type) estimator by using a coordinate scaling procedure rather than integration by parts, which allows more computational benefits. We also consider two different methods for treating the flux operator, i.e., local-path and global-path approaches, in which the latter achieves a smaller variance at the cost of using second-order potential derivatives. Numerical tests are performed for a one-dimensional Eckart barrier and a model proton transfer reaction in a polar solvent, which illustrates the reduced variance of the virial estimator over the corresponding thermodynamic estimator.
Israël, I; Grasso, R; Georges-Francois, P; Tsuzuku, T; Berthoz, A
1997-06-01
According to path integration, the brain is able to compute the distance of a traveled path. In this research we applied our previously reported method for studying memory of linear distance, a crucial mechanism in path integration; our method is based on the overt reconstruction of a passive transport. Passive transport is a special case of navigation in which no active control is performed. Blindfolded subjects were first asked to travel 2 m forward, in darkness, by driving with a joystick the robot on which they were seated. The results show that all subjects but two undershot this distance, i.e., overestimated their own displacement. Then, subjects were submitted to a passive linear forward displacement along 2, 4, 6, 8, or 10 m, and had to reproduce the same distance, still blindfolded. The results show that the distance of the stimulus was accurately reproduced, as well as stimulus duration, peak velocity, and velocity profile. In this first condition, the imposed velocity profile was triangular and therefore stimulus distance and duration were correlated. In a second condition, it was shown that distance was correctly reproduced also when the information about stimulus duration was kept constant. Here, different velocity profiles were used as stimuli, and most subjects also reproduced the velocity profile. Statistical analyses indicated that distance was not reproduced as a consequence of duration, peak velocity, or velocity profile reproduction, but was uniquely correlated to stimulus distance. The previous hypothesis of a double integration of the otolith signal to provide a distance estimate can explain our results. There was a large discrepancy between the accuracy with which the subjects matched the velocity profiles and that of distance reproduction. It follows that, whereas the dynamics of passive motion are stored and available to further use, distance is independently estimated. It is concluded that vestibular and somatosensory signals excited by
NASA Astrophysics Data System (ADS)
Yamamoto, Takeshi; Miller, William H.
2005-01-01
The quantum instanton approximation for thermal rate constants, a type of quantum transition state theory (QTST), is applied to a model proton transfer reaction in liquid methyl chloride developed by Azzouz and Borgis. Monte Carlo path integral methods are used to carry out the calculations, and two other closely related QTST's, namely, the centroid-density and Hansen-Andersen QTST, are also evaluated for comparison using the present path integral approach. A technique is then introduced that calculates the kinetic isotope effect directly via thermodynamic integration of the rate with respect to hydrogen mass, which has the practical advantage of avoiding costly evaluation of the activation free energy. The present application to the Azzouz-Borgis problem shows that the above three types of QTST provide very similar results for the rate, within 30% of each other, which is nontrivial considering the totally different derivations of these QTSTs; the latter rates are also in reasonable agreement with some other previous results (e.g., obtained via molecular dynamics with quantum transitions), within a factor of ˜2(7) for the H(D) transfer, thus significantly diminishing the possible range of the exact rates. In addition, it is revealed that a small but nonnegligible inconsistency exists in the parametrization of the Azzouz-Borgis model employed in previous studies, which resulted in the large apparent discrepancy in the calculated rates.
Dynamic response characteristics of dual flow-path integrally bladed rotors
NASA Astrophysics Data System (ADS)
Beck, Joseph A.; Brown, Jeffrey M.; Scott-Emuakpor, Onome E.; Cross, Charles J.; Slater, Joseph C.
2015-02-01
New turbine engine designs requiring secondary flow compression often look to dual flow-path integrally bladed rotors (DFIBRs) since these stages have the ability to perform work on the secondary, or bypassed, flow-field. While analogous to traditional integrally bladed rotor stages, DFIBR designs have many differences that result in unique dynamic response characteristics that must be understood to avoid fatigue. This work investigates these characteristics using reduced-order models (ROMs) that incorporate mistuning through perturbations to blade frequencies. This work provides an alternative to computationally intensive geometric-mistuning approaches for DFIBRs by utilizing tuned blade mode reductions and substructure coupling in cyclic coordinates. Free and forced response results are compared to full finite element model (FEM) solutions to determine if any errors are related to the reduced-order model formulation reduction methods. It is shown that DFIBRs have many more frequency veering regions than their single flow-path integrally blade rotor (IBR) counterparts. Modal families are shown to transition between system, inner-blade, and outer-blade motion. Furthermore, findings illustrate that while mode localization of traditional IBRs is limited to a single or small subset of blades, DFIBRs can have modal energy localized to either an inner- or outer-blade set resulting in many blades responding above tuned levels. Lastly, ROM forced response predictions compare well to full FEM predictions for the two test cases shown.
Geng, Hua Y.
2015-02-15
A multilevel approach to sample the potential energy surface in a path integral formalism is proposed. The purpose is to reduce the required number of ab initio evaluations of energy and forces in ab initio path integral molecular dynamics (AI-PIMD) simulation, without compromising the overall accuracy. To validate the method, the internal energy and free energy of an Einstein crystal are calculated and compared with the analytical solutions. As a preliminary application, we assess the performance of the method in a realistic model—the FCC phase of dense atomic hydrogen, in which the calculated result shows that the acceleration rate is about 3 to 4-fold for a two-level implementation, and can be increased up to 10 times if extrapolation is used. With only 16 beads used for the ab initio potential sampling, this method gives a well converged internal energy. The residual error in pressure is just about 3 GPa, whereas it is about 20 GPa for a plain AI-PIMD calculation with the same number of beads. The vibrational free energy of the FCC phase of dense hydrogen at 300 K is also calculated with an AI-PIMD thermodynamic integration method, which gives a result of about 0.51 eV/proton at a density of r{sub s}=0.912.
NASA Astrophysics Data System (ADS)
Minary, Peter; Martyna, Glenn J.; Tuckerman, Mark E.
2003-02-01
In this paper (Paper I) and a companion paper (Paper II), novel new algorithms and applications of the isokinetic ensemble as generated by Gauss' principle of least constraint, pioneered for use with molecular dynamics 20 years ago, are presented for biophysical, path integral, and Car-Parrinello based ab initio molecular dynamics. In Paper I, a new "extended system" version of the isokinetic equations of motion that overcomes the ergodicity problems inherent in the standard approach, is developed using a new theory of non-Hamiltonian phase space analysis [M. E. Tuckerman et al., Europhys. Lett. 45, 149 (1999); J. Chem. Phys. 115, 1678 (2001)]. Reversible multiple time step integrations schemes for the isokinetic methods, first presented by Zhang [J. Chem. Phys. 106, 6102 (1997)] are reviewed. Next, holonomic constraints are incorporated into the isokinetic methodology for use in fast efficient biomolecular simulation studies. Model and realistic examples are presented in order to evaluate, critically, the performance of the new isokinetic molecular dynamic schemes. Comparisons are made to the, now standard, canonical dynamics method, Nosé-Hoover chain dynamics [G. J. Martyna et al., J. Chem. Phys. 97, 2635 (1992)]. The new isokinetic techniques are found to yield more efficient sampling than the Nosé-Hoover chain method in both path integral molecular dynamics and biophysical molecular dynamics calculations. In Paper II, the use of isokinetic methods in Car-Parrinello based ab initio molecular dynamics calculations is presented.
NASA Astrophysics Data System (ADS)
Geng, Hua Y.
2015-02-01
A multilevel approach to sample the potential energy surface in a path integral formalism is proposed. The purpose is to reduce the required number of ab initio evaluations of energy and forces in ab initio path integral molecular dynamics (AI-PIMD) simulation, without compromising the overall accuracy. To validate the method, the internal energy and free energy of an Einstein crystal are calculated and compared with the analytical solutions. As a preliminary application, we assess the performance of the method in a realistic model-the FCC phase of dense atomic hydrogen, in which the calculated result shows that the acceleration rate is about 3 to 4-fold for a two-level implementation, and can be increased up to 10 times if extrapolation is used. With only 16 beads used for the ab initio potential sampling, this method gives a well converged internal energy. The residual error in pressure is just about 3 GPa, whereas it is about 20 GPa for a plain AI-PIMD calculation with the same number of beads. The vibrational free energy of the FCC phase of dense hydrogen at 300 K is also calculated with an AI-PIMD thermodynamic integration method, which gives a result of about 0.51 eV/proton at a density of rs = 0.912.
Hippocampus and Retrosplenial Cortex Combine Path Integration Signals for Successful Navigation
Erdem, Uğur M.; Ross, Robert S.; Brown, Thackery I.; Hasselmo, Michael E.; Stern, Chantal E.
2013-01-01
The current study used fMRI in humans to examine goal-directed navigation in an open field environment. We designed a task that required participants to encode survey-level spatial information and subsequently navigate to a goal location in either first person, third person, or survey perspectives. Critically, no distinguishing landmarks or goal location markers were present in the environment, thereby requiring participants to rely on path integration mechanisms for successful navigation. We focused our analysis on mechanisms related to navigation and mechanisms tracking linear distance to the goal location. Successful navigation required translation of encoded survey-level map information for orientation and implementation of a planned route to the goal. Our results demonstrate that successful first and third person navigation trials recruited the anterior hippocampus more than trials when the goal location was not successfully reached. When examining only successful trials, the retrosplenial and posterior parietal cortices were recruited for goal-directed navigation in both first person and third person perspectives. Unique to first person perspective navigation, the hippocampus was recruited to path integrate self-motion cues with location computations toward the goal location. Last, our results demonstrate that the hippocampus supports goal-directed navigation by actively tracking proximity to the goal throughout navigation. When using path integration mechanisms in first person and third person perspective navigation, the posterior hippocampus was more strongly recruited as participants approach the goal. These findings provide critical insight into the neural mechanisms by which we are able to use map-level representations of our environment to reach our navigational goals. PMID:24305826
Garberoglio, Giovanni; Jankowski, Piotr; Szalewicz, Krzysztof; Harvey, Allan H.
2014-07-28
We present a path-integral Monte Carlo procedure for the fully quantum calculation of the second molecular virial coefficient accounting for intramolecular flexibility. This method is applied to molecular hydrogen (H{sub 2}) and deuterium (D{sub 2}) in the temperature range 15–2000 K, showing that the effect of molecular flexibility is not negligible. Our results are in good agreement with experimental data, as well as with virials given by recent empirical equations of state, although some discrepancies are observed for H{sub 2} between 100 and 200 K.
Error Reduction Methods for Integrated-path Differential-absorption Lidar Measurements
NASA Technical Reports Server (NTRS)
Chen, Jeffrey R.; Numata, Kenji; Wu, Stewart T.
2012-01-01
We report new modeling and error reduction methods for differential-absorption optical-depth (DAOD) measurements of atmospheric constituents using direct-detection integrated-path differential-absorption lidars. Errors from laser frequency noise are quantified in terms of the line center fluctuation and spectral line shape of the laser pulses, revealing relationships verified experimentally. A significant DAOD bias is removed by introducing a correction factor. Errors from surface height and reflectance variations can be reduced to tolerable levels by incorporating altimetry knowledge and "log after averaging", or by pointing the laser and receiver to a fixed surface spot during each wavelength cycle to shorten the time of "averaging before log".
All-Electron Path Integral Simulations of Warm, Dense Matter: Application to Water and Carbon
NASA Astrophysics Data System (ADS)
Driver, Kevin; Militzer, Burkhard
2012-02-01
We develop an all-electron path integral Monte Carlo (PIMC) method for warm dense matter and apply it to study water and carbon. PIMC pressures, internal energies, and pair-correlation functions compare well with density functional theory molecular dynamics (DFT-MD) at lower temperatures and enable the construction of a coherent equation of state over a density-temperature range of 3--12 g/cm^3 and 10^2--10^9 K. PIMC results converge to the Debye-Huckel limiting law at high-temperatures and illuminate the breakdown of DFT pseudopotentials due to core excitations.
Path-integral calculation of the third virial coefficient of quantum gases at low temperatures
Garberoglio, Giovanni; Harvey, Allan H.
2011-04-07
We derive path-integral expressions for the second and third virial coefficients of monatomic quantum gases. Unlike previous work that considered only Boltzmann statistics, we include exchange effects (Bose-Einstein or Fermi-Dirac statistics). We use state-of-the-art pair and three-body potentials to calculate the third virial coefficient of {sup 3}He and {sup 4}He in the temperature range 2.6-24.5561 K. We obtain uncertainties smaller than those of the limited experimental data. Inclusion of exchange effects is necessary to obtain accurate results below about 7 K.
Path-integral calculation of the third virial coefficient of quantum gases at low temperatures.
Garberoglio, Giovanni; Harvey, Allan H
2011-04-07
We derive path-integral expressions for the second and third virial coefficients of monatomic quantum gases. Unlike previous work that considered only Boltzmann statistics, we include exchange effects (Bose-Einstein or Fermi-Dirac statistics). We use state-of-the-art pair and three-body potentials to calculate the third virial coefficient of (3)He and (4)He in the temperature range 2.6-24.5561 K. We obtain uncertainties smaller than those of the limited experimental data. Inclusion of exchange effects is necessary to obtain accurate results below about 7 K.
NASA Astrophysics Data System (ADS)
Garberoglio, Giovanni; Jankowski, Piotr; Szalewicz, Krzysztof; Harvey, Allan H.
2014-07-01
We present a path-integral Monte Carlo procedure for the fully quantum calculation of the second molecular virial coefficient accounting for intramolecular flexibility. This method is applied to molecular hydrogen (H2) and deuterium (D2) in the temperature range 15-2000 K, showing that the effect of molecular flexibility is not negligible. Our results are in good agreement with experimental data, as well as with virials given by recent empirical equations of state, although some discrepancies are observed for H2 between 100 and 200 K.
Garberoglio, Giovanni; Jankowski, Piotr; Szalewicz, Krzysztof; Harvey, Allan H
2014-07-28
We present a path-integral Monte Carlo procedure for the fully quantum calculation of the second molecular virial coefficient accounting for intramolecular flexibility. This method is applied to molecular hydrogen (H2) and deuterium (D2) in the temperature range 15-2000 K, showing that the effect of molecular flexibility is not negligible. Our results are in good agreement with experimental data, as well as with virials given by recent empirical equations of state, although some discrepancies are observed for H2 between 100 and 200 K.
Path integral representation of spin foam models of 4D gravity
NASA Astrophysics Data System (ADS)
Conrady, Florian; Freidel, Laurent
2008-12-01
We give a unified description of all recent spin foam models introduced by Engle, Livine, Pereira and Rovelli (ELPR) and by Freidel and Krasnov (FK). We show that the FK models are, for all values of the Immirzi parameter γ, equivalent to path integrals of a discrete theory and we provide an explicit formula for the associated actions. We discuss the relation between the FK and ELPR models and also study the corresponding boundary states. For general Immirzi parameter, these are given by Alexandrov's and Livine's SO(4) projected states. For 0 <= γ < 1, the states can be restricted to SU(2) spin networks.
Option pricing formulas and nonlinear filtering: a Feynman path integral perspective
NASA Astrophysics Data System (ADS)
Balaji, Bhashyam
2013-05-01
Many areas of engineering and applied science require the solution of certain parabolic partial differential equa tions, such as the Fokker-Planck and Kolmogorov equations. The fundamental solution, or the Green's function, for such PDEs can be written in terms of the Feynman path integral (FPI). The partial differential equation arising in the valuing of options is the Kolmogorov backward equation that is referred to as the Black-Scholes equation. The utility of this is demonstrated and numerical examples that illustrate the high accuracy of option price calculation even when using a fairly coarse grid.
Liu, Jian; Zhang, Zhijun
2016-01-21
Path integral Liouville dynamics (PILD) is applied to vibrational dynamics of several simple but representative realistic molecular systems (OH, water, ammonia, and methane). The dipole-derivative autocorrelation function is employed to obtain the infrared spectrum as a function of temperature and isotopic substitution. Comparison to the exact vibrational frequency shows that PILD produces a reasonably accurate peak position with a relatively small full width at half maximum. PILD offers a potentially useful trajectory-based quantum dynamics approach to compute vibrational spectra of molecular systems.
Temperature-dependent isovector pairing gap equations using a path integral approach
Fellah, M.; Allal, N. H.; Belabbas, M.; Oudih, M. R.; Benhamouda, N.
2007-10-15
Temperature-dependent isovector neutron-proton (np) pairing gap equations have been established by means of the path integral approach. These equations generalize the BCS ones for the pairing between like particles at finite temperature. The method has been numerically tested using the one-level model. It has been shown that the gap parameter {delta}{sub np} has a behavior analogous to that of {delta}{sub nn} and {delta}{sub pp} as a function of the temperature: one notes the presence of a critical temperature. Moreover, it has been shown that the isovector pairing effects remain beyond the critical temperature that corresponds to the pairing between like particles.
An introduction to stochastic control theory, path integrals and reinforcement learning
NASA Astrophysics Data System (ADS)
Kappen, Hilbert J.
2007-02-01
Control theory is a mathematical description of how to act optimally to gain future rewards. In this paper I give an introduction to deterministic and stochastic control theory and I give an overview of the possible application of control theory to the modeling of animal behavior and learning. I discuss a class of non-linear stochastic control problems that can be efficiently solved using a path integral or by MC sampling. In this control formalism the central concept of cost-to-go becomes a free energy and methods and concepts from statistical physics can be readily applied.
NASA Astrophysics Data System (ADS)
Artoun, Ojenie; David-Rus, Diana; Emmett, Matthew; Fishman, Lou; Fital, Sandra; Hogan, Chad; Lim, Jisun; Lushi, Enkeleida; Marinov, Vesselin
2006-05-01
In this report we summarize an extension of Fourier analysis for the solution of the wave equation with a non-constant coefficient corresponding to an inhomogeneous medium. The underlying physics of the problem is exploited to link pseudodifferential operators and phase space path integrals to obtain a marching algorithm that incorporates the backward scattering into the evolution of the wave. This allows us to successfully apply single-sweep, one-way marching methods in inherently two-way environments, which was not achieved before through other methods for this problem.
Liu, Jian; Zhang, Zhijun
2016-01-21
Path integral Liouville dynamics (PILD) is applied to vibrational dynamics of several simple but representative realistic molecular systems (OH, water, ammonia, and methane). The dipole-derivative autocorrelation function is employed to obtain the infrared spectrum as a function of temperature and isotopic substitution. Comparison to the exact vibrational frequency shows that PILD produces a reasonably accurate peak position with a relatively small full width at half maximum. PILD offers a potentially useful trajectory-based quantum dynamics approach to compute vibrational spectra of molecular systems.
NASA Astrophysics Data System (ADS)
Gangopadhyay, Sunandan
2015-06-01
We employ the path integral approach developed in Gangopadhyay S. and Scholtz F. E., Phys. Rev. Lett., 102 (2009) 241602 to discuss the (generalized) harmonic oscillator in a noncommutative plane. The action for this system is derived in the coherent state basis with additional degrees of freedom. From this the action in the coherent state basis without any additional degrees of freedom is obtained. This gives the ground-state spectrum of the system. We then employ the exact renormalization group approach to show that an equivalence can be constructed between this (noncommutative) system and a commutative system.
The chemical shift of deprotonated water dimer: Ab initio path integral simulation
NASA Astrophysics Data System (ADS)
Shiga, Motoyuki; Suzuki, Kimichi; Tachikawa, Masanori
2010-03-01
The H1 NMR chemical shift in deprotonated water dimer H3O2- has been studied by ab initio path integral simulation. The simulation predicts that the isotropic shielding of hydrogen-bonded proton increases as a function of temperature by about 0.003 ppm/K. This change is about an order of magnitude larger than that of the nonhydrogen-bonded proton. It is concluded that this is caused by the significant difference in the quantum distribution of proton at high and low temperatures in the low barrier hydrogen bond.
Local time of Lévy random walks: A path integral approach
NASA Astrophysics Data System (ADS)
Zatloukal, Václav
2017-05-01
The local time of a stochastic process quantifies the amount of time that sample trajectories x (τ ) spend in the vicinity of an arbitrary point x . For a generic Hamiltonian, we employ the phase-space path-integral representation of random walk transition probabilities in order to quantify the properties of the local time. For time-independent systems, the resolvent of the Hamiltonian operator proves to be a central tool for this purpose. In particular, we focus on the local times of Lévy random walks (Lévy flights), which correspond to fractional diffusion equations.
Ab initio Path Integral Molecular Dynamics Based on Fragment Molecular Orbital Method
NASA Astrophysics Data System (ADS)
Fujita, Takatoshi; Watanabe, Hirofumi; Tanaka, Shigenori
2009-10-01
We have developed an ab initio path integral molecular dynamics method based on the fragment molecular orbital method. This “FMO-PIMD” method can treat both nuclei and electrons quantum mechanically, and is useful to simulate large hydrogen-bonded systems with high accuracy. After a benchmark calculation for water monomer, water trimer and glycine pentamer have been studied using the FMO-PIMD method to investigate nuclear quantum effects on structure and molecular interactions. The applicability of the present approach is demonstrated through a number of test calculations.
Formation of bound states in expanded metal studied via path integral molecular dynamics
NASA Astrophysics Data System (ADS)
Deymier, P. A.; Oh, Ki-Dong
2004-03-01
The usefulness of the restricted path integral molecular dynamics method for the study of strongly correlated electrons is demonstrated by studying the formation of bound electronic states in a half-filled expanded three-dimensional hydrogenoid body-centred cubic lattice at finite temperature. Starting from a metallic state with one-component plasma character, we find that bound electrons form upon expansion of the lattice. The bound electrons are spatially localized with their centre for the motion of gyration located at ionic positions. The number of bound electrons increases monotonically with decreasing density.
NASA Astrophysics Data System (ADS)
Krajewski, Florian R.; Müser, Martin H.
2005-07-01
The spectral density of quantum mechanical Frenkel Kontorova chains moving in disordered, external potentials is investigated by means of path-integral molecular dynamics. If the second moment of the embedding potential is well defined (roughness exponent H=0), there is one regime in which the chain is pinned (large masses m of chain particles) and one in which it is unpinned (small m). If the embedding potential can be classified as a random walk on large length scales ( H=1/2), then the chain is always pinned irrespective of the value of m. For H=1/2, two phonon-like branches appear in the spectra.
Path-integral molecular dynamics simulations for water anion clusters (HO)5- and (DO)5-
NASA Astrophysics Data System (ADS)
Takayanagi, Toshiyuki; Yoshikawa, Takehiro; Motegi, Haruki; Shiga, Motoyuki
2009-11-01
Quantum path-integral molecular dynamics simulations have been performed for the (HO)5- and (DO)5- anion clusters on the basis of a semiempirical one-electron pseudopotential-polarization model. Due to larger zero-point vibrational amplitudes for H atoms than that of D atoms, hydrogen-bond lengths in the (HO)5- cluster are slightly larger than those in (DO)5-. The distribution of the vertical detachment energies for (HO)5- also show a broader feature than that for (DO)5-. The present PIMD simulations thus demonstrate the importance of nuclear quantum effects in water anion clusters.
NASA Astrophysics Data System (ADS)
Kapila, Vivek; Deymier, Pierre; Runge, Keith
2011-10-01
Several areas of study including heavy ion beam, large scale laser, and high pressure or Thomson scattering studies necessitate a fundamental understanding of warm dense matter (WDM) i.e. matter at high temperature and high density. The WDM regime, however, lacks any adequate highly developed class of simulation methods. Recent progress to address this deficit has been the development of orbital-free Density Functional Theory (ofDFT). However, scant benchmark information is available on temperature and pressure dependence of simple but realistic models in WDM regime. The present work aims to fill this critical gap using the restricted path-integral molecular dynamics (rPIMD) method. Within the discrete path integral representation, electrons are described as harmonic necklaces. Quantum exchange takes the form of cross linking between electron necklaces. The fermion sign problem is addressed by restricting the density matrix to positive values. The molecular dynamics algorithm is employed to sample phase space. Here, we focus on the behavior of strongly correlated electron plasmas under WDM conditions. We compute the kinetic and potential energies and compare them to those obtained with the ofDFT method. Several areas of study including heavy ion beam, large scale laser, and high pressure or Thomson scattering studies necessitate a fundamental understanding of warm dense matter (WDM) i.e. matter at high temperature and high density. The WDM regime, however, lacks any adequate highly developed class of simulation methods. Recent progress to address this deficit has been the development of orbital-free Density Functional Theory (ofDFT). However, scant benchmark information is available on temperature and pressure dependence of simple but realistic models in WDM regime. The present work aims to fill this critical gap using the restricted path-integral molecular dynamics (rPIMD) method. Within the discrete path integral representation, electrons are described as
Path Integral Molecular Dynamics for Hydrogen with Orbital-Free Density Functional Theory
NASA Astrophysics Data System (ADS)
Runge, Keith; Karasiev, Valentin; Deymier, Pierre
2014-03-01
The computational bottleneck for performing path-integral molecular dynamics (PIMD) for nuclei on a first principles electronic potential energy surface has been the speed with which forces from the electrons can be generated. Recent advances in orbital-free density functional theory (OF-DFT) not only allow for faster generation of first principles forces but also include the effects of temperature on the electron density. We will present results of calculations on hydrogen in warm dense matter conditions where the protons are described by PIMD and the electrons by OF-DFT. Work supported by U.S. Dept. of Energy, grant DE-SC0002139.
Unified path integral approach to theories of diffusion-influenced reactions
NASA Astrophysics Data System (ADS)
Prüstel, Thorsten; Meier-Schellersheim, Martin
2017-08-01
Building on mathematical similarities between quantum mechanics and theories of diffusion-influenced reactions, we develop a general approach for computational modeling of diffusion-influenced reactions that is capable of capturing not only the classical Smoluchowski picture but also alternative theories, as is here exemplified by a volume reactivity model. In particular, we prove the path decomposition expansion of various Green's functions describing the irreversible and reversible reaction of an isolated pair of molecules. To this end, we exploit a connection between boundary value and interaction potential problems with δ - and δ'-function perturbation. We employ a known path-integral-based summation of a perturbation series to derive a number of exact identities relating propagators and survival probabilities satisfying different boundary conditions in a unified and systematic manner. Furthermore, we show how the path decomposition expansion represents the propagator as a product of three factors in the Laplace domain that correspond to quantities figuring prominently in stochastic spatially resolved simulation algorithms. This analysis will thus be useful for the interpretation of current and the design of future algorithms. Finally, we discuss the relation between the general approach and the theory of Brownian functionals and calculate the mean residence time for the case of irreversible and reversible reactions.
Development of a Pulsed 2-Micron Integrated Path Differential Absorption Lidar for CO2 Measurement
NASA Technical Reports Server (NTRS)
Singh, Upendra N.; Yu, Jirong; Petros, Mulugeta; Refaat, Tamer; Refaat, Tamer
2013-01-01
Atmospheric carbon dioxide (CO2) is an important greenhouse gas that significantly contributes to the carbon cycle and global radiation budget on Earth. Active remote sensing of CO2 is important to address several limitations that contend with passive sensors. A 2-micron double-pulsed, Integrated Path Differential Absorption (IPDA) lidar instrument for ground and airborne atmospheric CO2 concentration measurements via direct detection method is being developed at NASA Langley Research Center. This active remote sensing instrument will provide an alternate approach of measuring atmospheric CO2 concentrations with significant advantages. A high energy pulsed approach provides high-precision measurement capability by having high signal-to-noise ratio level and unambiguously eliminates the contamination from aerosols and clouds that can bias the IPDA measurement. Commercial, on the shelf, components are implemented for the detection system. Instrument integration will be presented in this paper as well as a background for CO2 measurement at NASA Langley research Center
High-order sampling schemes for path integrals and Gaussian chain simulations of polymers
Müser, Martin H.; Müller, Marcus
2015-05-07
In this work, we demonstrate that path-integral schemes, derived in the context of many-body quantum systems, benefit the simulation of Gaussian chains representing polymers. Specifically, we show how to decrease discretization corrections with little extra computation from the usual O(1/P{sup 2}) to O(1/P{sup 4}), where P is the number of beads representing the chains. As a consequence, high-order integrators necessitate much smaller P than those commonly used. Particular emphasis is placed on the questions of how to maintain this rate of convergence for open polymers and for polymers confined by a hard wall as well as how to ensure efficient sampling. The advantages of the high-order sampling schemes are illustrated by studying the surface tension of a polymer melt and the interface tension in a binary homopolymers blend.
Development of a pulsed 2-micron integrated path differential absorption lidar for CO2 measurement
NASA Astrophysics Data System (ADS)
Singh, Upendra N.; Yu, Jirong; Petros, Mulugeta; Refaat, Tamer; Reithmaier, Karl
2013-09-01
Atmospheric carbon dioxide (CO2) is an important greenhouse gas that significantly contributes to the carbon cycle and global radiation budget on Earth. Active remote sensing of CO2 is important to address several limitations that contend with passive sensors. A 2-micron double-pulsed, Integrated Path Differential Absorption (IPDA) lidar instrument for ground and airborne atmospheric CO2 concentration measurements via direct detection method is being developed at NASA Langley Research Center. This active remote sensing instrument will provide an alternate approach of measuring atmospheric CO2 concentrations with significant advantages. A high energy pulsed approach provides high-precision measurement capability by having high signal-to-noise ratio level and unambiguously eliminates the contamination from aerosols and clouds that can bias the IPDA measurement. Commercial, on the shelf, components are implemented for the detection system. Instrument integration will be presented in this paper as well as a background for CO2 measurement at NASA Langley research Center.
A reductionist perspective on quantum statistical mechanics: Coarse-graining of path integrals.
Sinitskiy, Anton V; Voth, Gregory A
2015-09-07
Computational modeling of the condensed phase based on classical statistical mechanics has been rapidly developing over the last few decades and has yielded important information on various systems containing up to millions of atoms. However, if a system of interest contains important quantum effects, well-developed classical techniques cannot be used. One way of treating finite temperature quantum systems at equilibrium has been based on Feynman's imaginary time path integral approach and the ensuing quantum-classical isomorphism. This isomorphism is exact only in the limit of infinitely many classical quasiparticles representing each physical quantum particle. In this work, we present a reductionist perspective on this problem based on the emerging methodology of coarse-graining. This perspective allows for the representations of one quantum particle with only two classical-like quasiparticles and their conjugate momenta. One of these coupled quasiparticles is the centroid particle of the quantum path integral quasiparticle distribution. Only this quasiparticle feels the potential energy function. The other quasiparticle directly provides the observable averages of quantum mechanical operators. The theory offers a simplified perspective on quantum statistical mechanics, revealing its most reductionist connection to classical statistical physics. By doing so, it can facilitate a simpler representation of certain quantum effects in complex molecular environments.
A reductionist perspective on quantum statistical mechanics: Coarse-graining of path integrals
Sinitskiy, Anton V.; Voth, Gregory A.
2015-09-07
Computational modeling of the condensed phase based on classical statistical mechanics has been rapidly developing over the last few decades and has yielded important information on various systems containing up to millions of atoms. However, if a system of interest contains important quantum effects, well-developed classical techniques cannot be used. One way of treating finite temperature quantum systems at equilibrium has been based on Feynman’s imaginary time path integral approach and the ensuing quantum-classical isomorphism. This isomorphism is exact only in the limit of infinitely many classical quasiparticles representing each physical quantum particle. In this work, we present a reductionist perspective on this problem based on the emerging methodology of coarse-graining. This perspective allows for the representations of one quantum particle with only two classical-like quasiparticles and their conjugate momenta. One of these coupled quasiparticles is the centroid particle of the quantum path integral quasiparticle distribution. Only this quasiparticle feels the potential energy function. The other quasiparticle directly provides the observable averages of quantum mechanical operators. The theory offers a simplified perspective on quantum statistical mechanics, revealing its most reductionist connection to classical statistical physics. By doing so, it can facilitate a simpler representation of certain quantum effects in complex molecular environments.
Path integral representation of Lorentzian spinfoam model, asymptotics and simplicial geometries
NASA Astrophysics Data System (ADS)
Han, Muxin; Krajewski, Thomas
2014-01-01
A new path integral representation of Lorentzian Engle-Pereira-Rovelli-Livine spinfoam model is derived by employing the theory of unitary representation of {SL}(2, {C}). The path integral representation is taken as a starting point of semiclassical analysis. The relation between the spinfoam model and classical simplicial geometry is studied via the large-spin asymptotic expansion of the spinfoam amplitude with all spins uniformly large. More precisely, in the large-spin regime, there is an equivalence between the spinfoam critical configuration (with certain nondegeneracy assumption) and a classical Lorentzian simplicial geometry. Such an equivalence relation allows us to classify the spinfoam critical configurations by their geometrical interpretations, via two types of solution-generating maps. The equivalence between spinfoam critical configuration and simplical geometry also allows us to define the notion of globally oriented and time-oriented spinfoam critical configuration. It is shown that only at the globally oriented and time-oriented spinfoam critical configuration, the leading-order contribution of spinfoam large-spin asymptotics gives precisely an exponential of Lorentzian Regge action of General Relativity. At all other (unphysical) critical configurations, spinfoam large-spin asymptotics modifies the Regge action at the leading-order approximation.
Schütt, Ole; Sebastiani, Daniel
2013-04-05
We investigate the quantum-mechanical delocalization of hydrogen in rotational symmetric molecular systems. To this purpose, we perform ab initio path integral molecular dynamics simulations of a methanol molecule to characterize the quantum properties of hydrogen atoms in a representative system by means of their real-space and momentum-space densities. In particular, we compute the spherically averaged momentum distribution n(k) and the pseudoangular momentum distribution n(kθ). We interpret our results by comparing them to path integral samplings of a bare proton in an ideal torus potential. We find that the hydroxyl hydrogen exhibits a toroidal delocalization, which leads to characteristic fingerprints in the line shapes of the momentum distributions. We can describe these specific spectroscopic patterns quantitatively and compute their onset as a function of temperature and potential energy landscape. The delocalization patterns in the projected momentum distribution provide a promising computational tool to address the intriguing phenomenon of quantum delocalization in condensed matter and its spectroscopic characterization. As the momentum distribution n(k) is also accessible through Nuclear Compton Scattering experiments, our results will help to interpret and understand future measurements more thoroughly.
Interactions of the polarization and the sun compass in path integration of desert ants.
Lebhardt, Fleur; Ronacher, Bernhard
2014-08-01
Desert ants, Cataglyphis fortis, perform large-scale foraging trips in their featureless habitat using path integration as their main navigation tool. To determine their walking direction they use primarily celestial cues, the sky's polarization pattern and the sun position. To examine the relative importance of these two celestial cues, we performed cue conflict experiments. We manipulated the polarization pattern experienced by the ants during their outbound foraging excursions, reducing it to a single electric field (e-)vector direction with a linear polarization filter. The simultaneous view of the sun created situations in which the directional information of the sun and the polarization compass disagreed. The heading directions of the homebound runs recorded on a test field with full view of the natural sky demonstrate that none of both compasses completely dominated over the other. Rather the ants seemed to compute an intermediate homing direction to which both compass systems contributed roughly equally. Direct sunlight and polarized light are detected in different regions of the ant's compound eye, suggesting two separate pathways for obtaining directional information. In the experimental paradigm applied here, these two pathways seem to feed into the path integrator with similar weights.
Accelerating Ab Initio Path Integral Simulations via Imaginary Multiple-Timestepping.
Cheng, Xiaolu; Herr, Jonathan D; Steele, Ryan P
2016-04-12
This work investigates the use of multiple-timestep schemes in imaginary time for computationally efficient ab initio equilibrium path integral simulations of quantum molecular motion. In the simplest formulation, only every n(th) path integral replica is computed at the target level of electronic structure theory, whereas the remaining low-level replicas still account for nuclear motion quantum effects with a more computationally economical theory. Motivated by recent developments for multiple-timestep techniques in real-time classical molecular dynamics, both 1-electron (atomic-orbital basis set) and 2-electron (electron correlation) truncations are shown to be effective. Structural distributions and thermodynamic averages are tested for representative analytic potentials and ab initio molecular examples. Target quantum chemistry methods include density functional theory and second-order Møller-Plesset perturbation theory, although any level of theory is formally amenable to this framework. For a standard two-level splitting, computational speedups of 1.6-4.0x are observed when using a 4-fold reduction in time slices; an 8-fold reduction is feasible in some cases. Multitiered options further reduce computational requirements and suggest that quantum mechanical motion could potentially be obtained at a cost not significantly different from the cost of classical simulations.
NASA Astrophysics Data System (ADS)
Dvornikov, Maxim; Gitman, D. M.
2012-11-01
We study massive 1/2-spin particles in various external backgrounds keeping in mind applications to neutrino physics. We are mainly interested in massive Majorana (Weyl) fields. However, massive neutral Dirac particles are also considered. We formulate classical Lagrangian theory of the massive Weyl field in terms of Grassmann-odd two-component spinors. Then we construct the Hamiltonian formulation of such a theory, which turns out to be a theory with second-class constraints. Using this formulation we canonically quantize the massive free Weyl field. We derive propagators of the Weyl field and relate them to the propagator of a massive Dirac particle. We also study the massive Weyl particles propagating in the background mater. We find the path integral representation for the propagator of such a field, as well as the corresponding pseudoclassical particle action. The massless limit of the Weyl field interacting with the matter is considered and compared with results of other works. Finally, the path integral representation for the propagator of the neutral massive Dirac particle with an anomalous magnetic moment moving in the background matter and external electromagnetic field, as well as the corresponding pseudoclassical particle action are constructed.
van Zon, Ramses; Hernández de la Peña, Lisandro; Peslherbe, Gilles H; Schofield, Jeremy
2008-10-01
In this paper, the imaginary-time path-integral representation of the canonical partition function of a quantum system and nonequilibrium work fluctuation relations are combined to yield methods for computing free-energy differences in quantum systems using nonequilibrium processes. The path-integral representation is isomorphic to the configurational partition function of a classical field theory, to which a natural but fictitious Hamiltonian dynamics is associated. It is shown that if this system is prepared in an equilibrium state, after which a control parameter in the fictitious Hamiltonian is changed in a finite time, then formally the Jarzynski nonequilibrium work relation and the Crooks fluctuation relation hold, where work is defined as the change in the energy as given by the fictitious Hamiltonian. Since the energy diverges for the classical field theory in canonical equilibrium, two regularization methods are introduced which limit the number of degrees of freedom to be finite. The numerical applicability of the methods is demonstrated for a quartic double-well potential with varying asymmetry. A general parameter-free smoothing procedure for the work distribution functions is useful in this context.
Contact Potential Instability in the Path-Integral Description of Itinerant Ferromagnetism
NASA Astrophysics Data System (ADS)
Vermeyen, E.; Tempere, J.
2015-05-01
It has long been predicted that a two-component non-localized Fermi gas will exhibit spontaneous polarization for sufficiently strong repulsive interactions, a phenomenon which is called itinerant ferromagnetism. Recent experiments with ultracold atomic gases have reached the interaction strength for which theoretical models have predicted the occurrence of the normal-to-itinerant-ferromagnetic phase transition, but so far this transition has not been observed. The instability of the repulsive branch of the Feshbach resonance prevents the formation of the itinerant ferromagnetic state, but it is not clear whether this is the only instability impeding its experimental realization. In this article, we use the path-integral formalism with density fields in the Hubbard-Stratonovich transformation to study the stability of a homogeneous two-component Fermi gas with contact interactions. Within the saddle-point approximation we show that none of the extrema of the action are minima, meaning all extrema are unstable to small density fluctuations. This implies a more general mechanical instability of the polarized (itinerant ferromagnetic) and normal states of the system in the path-integral formalism. We find that it is important to consider the stability of the system when studying itinerant ferromagnetism. Since (mechanical) stability may be influenced by the details of the interaction potential, we suggest the use of a more realistic potential than the contact potential in future theoretical descriptions.
Path integral method for predicting relative binding affinities of protein-ligand complexes
Mulakala, Chandrika; Kaznessis, Yiannis N.
2009-01-01
We present a novel approach for computing biomolecular interaction binding affinities based on a simple path integral solution of the Fokker-Planck equation. Computing the free energy of protein-ligand interactions can expedite structure-based drug design. Traditionally, the problem is seen through the lens of statistical thermodynamics. The computations can become, however, prohibitively long for the change in the free energy upon binding to be determined accurately. In this work we present a different approach based on a stochastic kinetic formalism. Inspired by Feynman's path integral formulation, we extend the theory to classical interacting systems. The ligand is modeled as a Brownian particle subjected to the effective non-bonding interaction potential of the receptor. This allows the calculation of the relative binding affinities of interacting biomolecules in water to be computed as a function of the ligand's diffusivity and the curvature of the potential surface in the vicinity of the binding minimum. The calculation is thus exceedingly rapid. In test cases, the correlation coefficient between actual and computed free energies is >0.93 for accurate data-sets. PMID:19275144
NASA Astrophysics Data System (ADS)
Barth, A. M.; Vagov, A.; Axt, V. M.
2016-09-01
We present a numerical path-integral iteration scheme for the low-dimensional reduced density matrix of a time-dependent quantum dissipative system. Our approach simultaneously accounts for the combined action of a microscopically modeled pure-dephasing-type coupling to a continuum of harmonic oscillators representing, e.g., phonons, and further environmental interactions inducing non-Hamiltonian dynamics in the inner system represented, e.g., by Lindblad-type dissipation or relaxation. Our formulation of the path-integral method allows for a numerically exact treatment of the coupling to the oscillator modes and moreover is general enough to provide a natural way to include Markovian processes that are sufficiently described by rate equations. We apply this new formalism to a model of a single semiconductor quantum dot which includes the coupling to longitudinal acoustic phonons for two cases: (a) external laser excitation taking into account a phenomenological radiative decay of the excited dot state and (b) a coupling of the quantum dot to a single mode of an optical cavity taking into account cavity photon losses.
Transport properties of liquid para-hydrogen: The path integral centroid molecular dynamics approach
NASA Astrophysics Data System (ADS)
Yonetani, Yoshiteru; Kinugawa, Kenichi
2003-11-01
Several fundamental transport properties of a quantum liquid para-hydrogen (p-H2) at 17 K have been numerically evaluated by means of the quantum dynamics simulation called the path integral centroid molecular dynamics (CMD). For comparison, classical molecular dynamics (MD) simulations have also been performed under the same condition. In accordance with the previous path integral simulations, the calculated static properties of the liquid agree well with the experimental results. For the diffusion coefficient, thermal conductivity, and shear viscosity, the CMD predicts the values closer to the experimental ones though the classical MD results are far from the reality. The agreement of the CMD result with the experimental one is especially good for the shear viscosity with the difference less than 5%. The calculated diffusion coefficient and the thermal conductivity agree with the experimental values at least in the same order. We predict that the ratio of bulk viscosity to shear viscosity for liquid p-H2 is much larger than classical van der Waals simple liquids such as rare gas liquids.
Tansey, Timothy N; Iwanaga, Kanako; Bezyak, Jill; Ditchman, Nicole
2017-05-04
Individuals with disabilities are more likely to live in poverty, have more health issues, and be less likely to be employed than their same-aged peers. Although these issues may be attenuated by vocational rehabilitation services, amotivation and ambivalence to employment can limit the readiness of persons with disabilities to engage in these services. Drawing on self-efficacy, self-determination, and stages of change theories, the purpose of this study was to develop and test an integrated self-determined work motivation model for people with disabilities. Participants included 277 people with disabilities recruited through vocational rehabilitation agencies across 8 states. Path analysis was used to evaluate the contribution of functional disability, self-determination, and social efficacy variables in a hypothesized integrated self-determined work motivation model. Model estimations used maximum likelihood estimation and model-data fit was examined using several goodness-of-fit indices. The initial path analysis indicated a less than optimal fit between the model and the observed data. Post hoc model modifications were conducted based on examination of the critical ratios and modification indices and theoretical consideration. The respecified integrated self-determined work motivation model fit the data very well, χ2/df = 1.88, CFI = .99, and RMSEA = 0.056. The R2 for the endogenous variables in the model ranged from .19 to .54. Findings from this study support the integrated self-determined work motivation model in vocational rehabilitation as a useful framework for understanding the relationship among functioning levels, self-determination and self-efficacy factors, vocational rehabilitation engagement, and readiness for employment. (PsycINFO Database Record (c) 2017 APA, all rights reserved).
Wolbers, Thomas; Wiener, Jan M; Mallot, Hanspeter A; Büchel, Christian
2007-08-29
Path integration, the ability to sense self-motion for keeping track of changes in orientation and position, constitutes a fundamental mechanism of spatial navigation and a keystone for the development of cognitive maps. Whereas animal path integration is predominantly supported by the head-direction, grid, and place cell systems, the neural foundations are not well understood in humans. Here we used functional magnetic resonance imaging and a virtual rendition of a triangle completion paradigm to test whether human path integration recruits a cortical system similar to that of rodents and nonhuman primates. Participants traveled along two legs of a triangle before pointing toward the starting location. In accordance with animal models, stronger right hippocampal activation predicted more accurate updating of the starting location on a trial-by-trial basis. Moreover, between-subjects fluctuations in response consistency were negatively correlated with bilateral hippocampal and medial prefrontal activation, and bilateral recruitment of the human motion complex (hMT+) covaried with individual path integration capability. Given that these effects were absent in a perceptual control task, the present study provides the first evidence that visual path integration is related to the dynamic interplay of self-motion processing in hMT+, higher-level spatial processes in the hippocampus, and spatial working memory in medial prefrontal cortex.
Tanizaki, Yuya; Koike, Takayuki
2014-12-15
Picard–Lefschetz theory is applied to path integrals of quantum mechanics, in order to compute real-time dynamics directly. After discussing basic properties of real-time path integrals on Lefschetz thimbles, we demonstrate its computational method in a concrete way by solving three simple examples of quantum mechanics. It is applied to quantum mechanics of a double-well potential, and quantum tunneling is discussed. We identify all of the complex saddle points of the classical action, and their properties are discussed in detail. However a big theoretical difficulty turns out to appear in rewriting the original path integral into a sum of path integrals on Lefschetz thimbles. We discuss generality of that problem and mention its importance. Real-time tunneling processes are shown to be described by those complex saddle points, and thus semi-classical description of real-time quantum tunneling becomes possible on solid ground if we could solve that problem. - Highlights: • Real-time path integral is studied based on Picard–Lefschetz theory. • Lucid demonstration is given through simple examples of quantum mechanics. • This technique is applied to quantum mechanics of the double-well potential. • Difficulty for practical applications is revealed, and we discuss its generality. • Quantum tunneling is shown to be closely related to complex classical solutions.
NASA Astrophysics Data System (ADS)
Douglas, Jack
2014-03-01
One of the things that puzzled me when I was a PhD student working under Karl Freed was the curious unity between the theoretical descriptions of excluded volume interactions in polymers, the hydrodynamic properties of polymers in solution, and the critical properties of fluid mixtures, gases and diverse other materials (magnets, superfluids,etc.) when these problems were formally expressed in terms of Wiener path integration and the interactions treated through a combination of epsilon expansion and renormalization group (RG) theory. It seemed that only the interaction labels changed from one problem to the other. What do these problems have in common? Essential clues to these interrelations became apparent when Karl Freed, myself and Shi-Qing Wang together began to study polymers interacting with hyper-surfaces of continuously variable dimension where the Feynman perturbation expansions could be performed through infinite order so that we could really understand what the RG theory was doing. It is evidently simply a particular method for resuming perturbation theory, and former ambiguities no longer existed. An integral equation extension of this type of exact calculation to ``surfaces'' of arbitrary fixed shape finally revealed the central mathematical object that links these diverse physical models- the capacity of polymer chains, whose value vanishes at the critical dimension of 4 and whose magnitude is linked to the friction coefficient of polymer chains, the virial coefficient of polymers and the 4-point function of the phi-4 field theory,...Once this central object was recognized, it then became possible solve diverse problems in material science through the calculation of capacity, and related ``virials'' properties, through Monte Carlo sampling of random walk paths. The essential ideas of this computational method are discussed and some applications given to non-trivial problems: nanotubes treated as either rigid rods or ensembles worm-like chains having
Zheng, Zewei; Zou, Yao
2016-11-01
This paper investigates the path following control problem for an unmanned airship in the presence of unknown wind and uncertainties. The backstepping technique augmented by a robust adaptive radial basis function neural network (RBFNN) is employed as the main control framework. Based on the horizontal dynamic model of the airship, an improved adaptive integral line-of-sight (LOS) guidance law is first proposed, which suits any parametric paths. The guidance law calculates the desired yaw angle and estimates the wind. Then the controller is extended to cope with the airship yaw tracking and velocity control by resorting to the augmented backstepping technique. The uncertainties of the dynamics are compensated by using the robust RBFNNs. Each robust RBFNN utilizes an nth-order smooth switching function to combine a conventional RBFNN with a robust control. The conventional RBFNN dominates in the neural active region, while the robust control retrieves the transient outside the active region, so that the stability range can be widened. Stability analysis shows that the controlled closed-loop system is globally uniformly ultimately bounded. Simulations are provided to validate the effectiveness of the proposed control approach. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.
Path integral centroid variables and the formulation of their exact real time dynamics
NASA Astrophysics Data System (ADS)
Jang, Seogjoo; Voth, Gregory A.
1999-08-01
A formalism is presented in this paper which, for the first time, establishes the theoretical basis for the quantum time evolution of path integral centroid variables and also provides clear motivation for using these variables to study condensed phase quantum dynamics. The equilibrium centroid distribution is first shown to be a well-defined distribution function which is specific to the canonical density operator. A quantum mechanical quasi-density operator (QDO) is associated with each value of the distribution so that, upon application of the standard quantum mechanical formalism, the QDO can be used to provide a rigorous definition of both static and dynamical centroid variables. Various properties of the dynamical centroid variables are derived, including the perspective that the centroid constraint on the imaginary time paths introduces a nonstationarity in the equilibrium ensemble which, in turn, can be shown to yield information on the correlations of spontaneous fluctuations. The analytic solution for the harmonic oscillator and a numerical solution for a double well system are provided which illustrate the various aspects of the theory. The theory contained herein provides the basis for a derivation of Centroid Molecular Dynamics, as well as the systematic improvements of that theory.
Information Entropy Exchange in the Path Integral Formulation of Transition Amplitudes
NASA Astrophysics Data System (ADS)
Deeter, Daniel; Petridis, Athanasios
2016-09-01
The quantum mechanical transition amplitude for a free particle is calculated using the path integral formalism. This amplitude is the kernel of the Schrödinger equation. A Wick rotation of the time increment transforms the kernel into a partition function that depends on the space and time intervals of the transition, with the temperature being proportional to the inverse of the time increment. The information entropy exchange between the system and the observer during the transition is calculated from the partition function. The requirement that this be real-valued leads to uncertainty-type relations. Furthermore, the transition exhibits positive information entropy exchange for small time intervals and negative entropy for large ones. The related statistical weight is inversely proportional to the square root of the time interval. Calculations for interacting systems are in progress.
Path integral study of the correlated electronic states of Na4-Na6
NASA Astrophysics Data System (ADS)
Hall, Randall W.
1990-12-01
Feynman's path integral formulation of quantum mechanics is used to study the correlated electronic states of Na4-Na6. Two types of simulations are performed: in the first, the nuclei are allowed to move at finite temperature in order to find the most stable geometries. In agreement with previous calculations, we find that planar structures are the most stable and that there is significant vibrational amplitude at finite temperatures, indicating that the Born-Oppenheimer surface is relatively flat. In the second type of simulation, the nuclei are held fixed at symmetric and asymmetric geometries and the correlated electron density is found. Our results show that the electrons are localized, rather than delocalized as previous workers have concluded from examination of the single-particle orbitals. We find that the best picture of these clusters is that they contain three-center, two-electron bonds.
All-Electron Path Integral Simulations of Warm, Dense Matter: Application to Water and Carbon
NASA Astrophysics Data System (ADS)
Driver, K. P.; Militzer, B.
2012-12-01
We develop an all-electron path integral Monte Carlo (PIMC) method for warm dense matter and apply it to study water and carbon. PIMC pressures, internal energies, and pair-correlation functions compare well with density functional theory molecular dynamics (DFT-MD) at lower temperatures and enable the construction of a coherent equation of state over a density-temperature range of 3--12 g/cm3 and 102--109 K. PIMC results converge to the Debye-Huckel limiting law at high-temperatures and illuminate the breakdown of DFT pseudopotentials due to core excitations. Funding provided by the NSF (DMS-1025370). Computational resources provided by the National Center for Atmospheric Research and Lawrence Berkeley National Laboratory.
Torsional path integral Monte Carlo method for the quantum simulation of large molecules
NASA Astrophysics Data System (ADS)
Miller, Thomas F.; Clary, David C.
2002-05-01
A molecular application is introduced for calculating quantum statistical mechanical expectation values of large molecules at nonzero temperatures. The Torsional Path Integral Monte Carlo (TPIMC) technique applies an uncoupled winding number formalism to the torsional degrees of freedom in molecular systems. The internal energy of the molecules ethane, n-butane, n-octane, and enkephalin are calculated at standard temperature using the TPIMC technique and compared to the expectation values obtained using the harmonic oscillator approximation and a variational technique. All studied molecules exhibited significant quantum mechanical contributions to their internal energy expectation values according to the TPIMC technique. The harmonic oscillator approximation approach to calculating the internal energy performs well for the molecules presented in this study but is limited by its neglect of both anharmonicity effects and the potential coupling of intramolecular torsions.
Quantum Mechanical Single Molecule Partition Function from PathIntegral Monte Carlo Simulations
Chempath, Shaji; Bell, Alexis T.; Predescu, Cristian
2006-10-01
An algorithm for calculating the partition function of a molecule with the path integral Monte Carlo method is presented. Staged thermodynamic perturbation with respect to a reference harmonic potential is utilized to evaluate the ratio of partition functions. Parallel tempering and a new Monte Carlo estimator for the ratio of partition functions are implemented here to achieve well converged simulations that give an accuracy of 0.04 kcal/mol in the reported free energies. The method is applied to various test systems, including a catalytic system composed of 18 atoms. Absolute free energies calculated by this method lead to corrections as large as 2.6 kcal/mol at 300 K for some of the examples presented.
A PATH INTEGRAL FORMULATION OF THE WRIGHT-FISHER PROCESS WITH GENIC SELECTION
SCHRAIBER, JOSHUA G.
2014-01-01
The Wright-Fisher process with selection is an important tool in population genetics theory. Traditional analysis of this process relies on the diffusion approximation. The diffusion approximation is usually studied in a partial differential equations framework. In this paper, I introduce a path integral formalism to study the Wright-Fisher process with selection and use that formalism to obtain a simple perturbation series to approximate the transition density. The perturbation series can be understood in terms of Feynman diagrams, which have a simple probabilistic interpretation in terms of selective events. The perturbation series proves to be an accurate approximation of the transition density for weak selection and is shown to be arbitrarily accurate for any selection coefficient. PMID:24269333
Euclidean path integral formalism in deformed space with minimum measurable length
NASA Astrophysics Data System (ADS)
Bernardo, Reginald Christian S.; Esguerra, Jose Perico H.
2017-04-01
We study time-evolution at the quantum level by developing the Euclidean path-integral approach for the general case where there exists a minimum measurable length. We derive an expression for the momentum-space propagator which turns out to be consistent with recently developed β-canonical transformation. We also construct the propagator for maximal localization which corresponds to the amplitude that a state which is maximally localized at location ξ' propagates to a state which is maximally localized at location ξ″ in a given time. Our expression for the momentum-space propagator and the propagator for maximal localization is valid for any form of time-independent Hamiltonian. The nonrelativistic free particle, particle in a linear potential, and the harmonic oscillator are discussed as examples.
Path integral centroid molecular dynamics simulation of para-hydrogen sandwiched by graphene sheets
NASA Astrophysics Data System (ADS)
Minamino, Yuki; Kinugawa, Kenichi
2016-11-01
The carbon-hydrogen composite systems of para-hydrogen (p-H2) sandwiched by a couple of graphene sheets have been investigated by means of path integral centroid molecular dynamics simulations at 17 K. It has been shown that sandwiched hydrogen is liquid-like but p-H2 molecules are preferably adsorbed onto the graphene sheets because of attractive graphene-hydrogen interaction. The diffusion coefficient of p-H2 molecules in the direction parallel to the graphene sheets is comparable to that in pure liquid p-H2. There exists a characteristic mode of 140 cm-1 of the p-H2 molecules, attributed to adsorption-binding motion perpendicular to the graphene sheets.
Path-integral Monte Carlo simulation of the warm dense homogeneous electron gas.
Brown, Ethan W; Clark, Bryan K; DuBois, Jonathan L; Ceperley, David M
2013-04-05
We perform calculations of the 3D finite-temperature homogeneous electron gas in the warm-dense regime (r(s) ≡ (3/4πn)(1/3)a(0)(-1) = 1.0-40.0 and Θ ≡ T/T(F) = 0.0625-8.0) using restricted path-integral Monte Carlo simulations. Precise energies, pair correlation functions, and structure factors are obtained. For all densities, we find a significant discrepancy between the ground state parametrized local density approximation and our results around T(F). These results can be used as a benchmark for developing finite-temperature density functionals, as well as input for orbital-free density function theory formulations.
A Path Integral Approach to Option Pricing with Stochastic Volatility: Some Exact Results
NASA Astrophysics Data System (ADS)
Baaquie, Belal E.
1997-12-01
The Black-Scholes formula for pricing options on stocks and other securities has been generalized by Merton and Garman to the case when stock volatility is stochastic. The derivation of the price of a security derivative with stochastic volatility is reviewed starting from the first principles of finance. The equation of Merton and Garman is then recast using the path integration technique of theoretical physics. The price of the stock option is shown to be the analogue of the Schrödinger wavefunction of quantum mechanics and the exact Hamiltonian and Lagrangian of the system is obtained. The results of Hull and White are generalized to the case when stock price and volatility have non-zero correlation. Some exact results for pricing stock options for the general correlated case are derived.
Excitonic effects in two-dimensional semiconductors: Path integral Monte Carlo approach
Velizhanin, Kirill A.; Saxena, Avadh
2015-11-01
The most striking features of novel two-dimensional semiconductors (e.g., transition metal dichalcogenide monolayers or phosphorene) is a strong Coulomb interaction between charge carriers resulting in large excitonic effects. In particular, this leads to the formation of multicarrier bound states upon photoexcitation (e.g., excitons, trions, and biexcitons), which could remain stable at near-room temperatures and contribute significantly to the optical properties of such materials. In our work we have used the path integral Monte Carlo methodology to numerically study properties of multicarrier bound states in two-dimensional semiconductors. Specifically, we have accurately investigated and tabulated the dependence of single-exciton, trion, and biexcitonmore » binding energies on the strength of dielectric screening, including the limiting cases of very strong and very weak screening. Our results of this work are potentially useful in the analysis of experimental data and benchmarking of theoretical and computational models.« less
Excitonic effects in two-dimensional semiconductors: Path integral Monte Carlo approach
Velizhanin, Kirill A.; Saxena, Avadh
2015-11-01
The most striking features of novel two-dimensional semiconductors (e.g., transition metal dichalcogenide monolayers or phosphorene) is a strong Coulomb interaction between charge carriers resulting in large excitonic effects. In particular, this leads to the formation of multicarrier bound states upon photoexcitation (e.g., excitons, trions, and biexcitons), which could remain stable at near-room temperatures and contribute significantly to the optical properties of such materials. In our work we have used the path integral Monte Carlo methodology to numerically study properties of multicarrier bound states in two-dimensional semiconductors. Specifically, we have accurately investigated and tabulated the dependence of single-exciton, trion, and biexciton binding energies on the strength of dielectric screening, including the limiting cases of very strong and very weak screening. Our results of this work are potentially useful in the analysis of experimental data and benchmarking of theoretical and computational models.
NASA Astrophysics Data System (ADS)
Voronov, Aleksandr V.; Tret'yakov, Evgeniy V.; Shuvalov, Vladimir V.
2004-06-01
Based on the path-integration technique and the Metropolis method, the original calculation scheme is developed for solving the problem of light propagation through highly scattering objects. The elimination of calculations of 'unnecessary' realisations and the phenomenological description of processes of multiple small-angle scattering provided a drastic increase (by nine and more orders of magnitude) in the calculation rate, retaining the specific features of the problem (consideration of spatial inhomogeneities, boundary conditions, etc.). The scheme allows one to verify other fast calculation algorithms and to obtain information required to reconstruct the internal structure of highly scattering objects (of size ~1000 scattered lengths and more) by the method of diffusion optical tomography.
Path integration: how the head direction signal maintains and corrects spatial orientation
Valerio, Stephane; Taube, Jeffrey S.
2012-01-01
Head direction (HD) cells have frequently been regarded as an internal “compass” that can be used for navigation, although there is little evidence showing a link between their activity and spatial behaviour. In a navigational task requiring the use of internal cues to return to a home base location without vision (path integration), we found a robust correlation between HD cell activity and the rat's heading error in their homing behaviour. Furthermore, we observed two different correction processes that animals used to improve performance after an error. The more frequent one consists of `resetting' the cell whenever the animal returns to the home location. However, we found that when large errors occur the HD system has the ability to `remap' and set a new reference frame, which is then used in subsequent trials. We also offer some insight into how these two correction processes operate when animals make an error. PMID:22983210
Time travel paradoxes, path integrals, and the many worlds interpretation of quantum mechanics
NASA Astrophysics Data System (ADS)
Everett, Allen
2004-06-01
We consider two approaches to evading paradoxes in quantum mechanics with closed timelike curves. In a model similar to Politzer’s, assuming pure states and using path integrals, we show that the problems of paradoxes and of unitarity violation are related; preserving unitarity avoids paradoxes by modifying the time evolution so that improbable events become certain. Deutsch has argued, using the density matrix, that paradoxes do not occur in the “many worlds interpretation.” We find that in this approach account must be taken of the resolution time of the device that detects objects emerging from a wormhole or other time machine. When this is done one finds that this approach is viable only if macroscopic objects traversing a wormhole interact with it so strongly that they are broken into microscopic fragments.
NASA Astrophysics Data System (ADS)
Larkin, A. S.; Filinov, V. S.; Fortov, V. E.
2016-11-01
The new numerical version of the Wigner approach to quantum mechanics for treatment thermodynamic properties of the strongly interacting systems of particles has been developed for extreme conditions, when there are no small physical parameters and analytical approximations used in different kind of perturbation theories can not be applied. The new path integral representation of the quantum Wigner function in the phase space has been developed for canonical ensemble. Explicit analytical expression of the Wigner function has been obtained in linear and harmonic approximations. The new quantum Monte-Carlo method for calculations of average values of arbitrary quantum operators has been proposed. Preliminary calculations of the momentum distribution function of the Coulomb systems of particles have been carried out. Comparison with classical Maxwell-Boltzmann distribution shows the significant influence of quantum effects on the high energy asymptotics (“tails’) of the calculated momentum distribution functions, which resulted in appearance of sharp oscillations.
Ultra-light and strong: The massless harmonic oscillator and its singular path integral
NASA Astrophysics Data System (ADS)
Modanese, Giovanni
2017-09-01
In classical mechanics, a light particle bound by a strong elastic force just oscillates at high frequency in the region allowed by its initial position and velocity. In quantum mechanics, instead, the ground state of the particle becomes completely de-localized in the limit m → 0. The harmonic oscillator thus ceases to be a useful microscopic physical model in the limit m → 0, but its Feynman path integral has interesting singularities which make it a prototype of other systems exhibiting a “quantum runaway” from the classical configurations near the minimum of the action. The probability density of the coherent runaway modes can be obtained as the solution of a Fokker-Planck equation associated to the condition S = Smin. This technique can be applied also to other systems, notably to a dimensional reduction of the Einstein-Hilbert action.
NASA Astrophysics Data System (ADS)
Lee, Mi Kyung; Huo, Pengfei; Coker, David F.
2016-05-01
This article reviews recent progress in the theoretical modeling of excitation energy transfer (EET) processes in natural light harvesting complexes. The iterative partial linearized density matrix path-integral propagation approach, which involves both forward and backward propagation of electronic degrees of freedom together with a linearized, short-time approximation for the nuclear degrees of freedom, provides an accurate and efficient way to model the nonadiabatic quantum dynamics at the heart of these EET processes. Combined with a recently developed chromophore-protein interaction model that incorporates both accurate ab initio descriptions of intracomplex vibrations and chromophore-protein interactions treated with atomistic detail, these simulation tools are beginning to unravel the detailed EET pathways and relaxation dynamics in light harvesting complexes.
WORM ALGORITHM PATH INTEGRAL MONTE CARLO APPLIED TO THE 3He-4He II SANDWICH SYSTEM
NASA Astrophysics Data System (ADS)
Al-Oqali, Amer; Sakhel, Asaad R.; Ghassib, Humam B.; Sakhel, Roger R.
2012-12-01
We present a numerical investigation of the thermal and structural properties of the 3He-4He sandwich system adsorbed on a graphite substrate using the worm algorithm path integral Monte Carlo (WAPIMC) method [M. Boninsegni, N. Prokof'ev and B. Svistunov, Phys. Rev. E74, 036701 (2006)]. For this purpose, we have modified a previously written WAPIMC code originally adapted for 4He on graphite, by including the second 3He-component. To describe the fermions, a temperature-dependent statistical potential has been used. This has proven very effective. The WAPIMC calculations have been conducted in the millikelvin temperature regime. However, because of the heavy computations involved, only 30, 40 and 50 mK have been considered for the time being. The pair correlations, Matsubara Green's function, structure factor, and density profiles have been explored at these temperatures.
Approximate path integral solution for a Dirac particle in a deformed Hulthén potential
NASA Astrophysics Data System (ADS)
Kadja, A.; Benamira, F.; Guechi, L.
2017-05-01
The problem of a Dirac particle moving in a deformed Hulthén potential is solved in the framework of the path integral formalism. With the help of the Biedenharn transformation, the construction of a closed form for the Green's function of the second-order Dirac equation is done by using a proper approximation to the centrifugal term and the Green's function of the linear Dirac equation is calculated. The energy spectrum for the bound states is obtained from the poles of the Green's function. A Dirac particle in the standard Hulthén potential ( q = 1) and a Dirac hydrogen-like ion ( q = 1 and a → ∞) are considered as particular cases.
Gaussian white noise analysis and its application to Feynman path integral
NASA Astrophysics Data System (ADS)
Suryawan, Herry Pribawanto
2016-02-01
In applied science, Gaussian white noise (the time derivative of Brownian motion) is often chosen as a mathematical idealization of phenomena involving sudden and extremely large fluctuations. It is also possible to define and study Gaussian white noise in a mathematically rigorous framework. In this survey paper we review the Gaussian white noise as an object in an infinite dimensional topological vector space. A brief construction of Gaussian white noise space and Gaussian white noise distributions will be presented. Gaussian white noise analysis provides a framework which offers various generalization of concept known from finite dimensional analysis to the infinite dimensional case, among them are differential operators, Fourier transform, and distribution theory. We will also present some recent developments and results on the application of Gaussian white noise theory to Feynman's path integral approach for quantum mechanics.
Path integration: how the head direction signal maintains and corrects spatial orientation.
Valerio, Stephane; Taube, Jeffrey S
2012-10-01
Head-direction cells have frequently been regarded as an internal 'compass' that can be used for navigation, although there is little evidence showing a link between their activity and spatial behavior. In a navigational task requiring the use of internal cues to return to a home location without vision (path integration), we found a robust correlation between head-direction cell activity and the rat's heading error in the rat's homing behavior. We observed two different correction processes that rats used to improve performance after an error. The more frequent one consists of 'resetting' the cell whenever the rat returns to the home location. However, we found that when large errors occur, the head-direction system has the ability to 'remap' and set a new reference frame, which is then used in subsequent trials. We also offer some insight into how these two correction processes operate when rats make an error.
Durlak, Piotr; Latajka, Zdzisław
2011-09-01
The double proton transfer process in the cyclic dimer of propionic acid in the gas phase was studied using a path integral molecular dynamics method. Structures, energies and proton trajectories were determined. Very large amplitude motions of the skeleton of a propionic acid molecule were observed during the simulations, and almost free rotation of the C(2)H(5) group around the C(α)-C bond. A double-well symmetric potential with a very small energy barrier was determined from the free energy profile for the proton motions. Infrared spectra for different isotopomers were calculated, and comparative vibrational analysis was performed. The vibrational results from CPMD appear to be in qualitative agreement with the experimental ones.
Systematic speedup of path integrals of a generic N-fold discretized theory
Bogojevic, A.; Balaz, A.; Belic, A.
2005-08-01
We present and discuss a detailed derivation of an analytical method that systematically improves the convergence of path integrals of a generic N-fold discretized theory. We develop an explicit procedure for calculating a set of effective actions S{sup (p)}, for p=1,2,3,... which have the property that they lead to the same continuum amplitudes as the starting action, but converge to that continuum limit ever faster. Discretized amplitudes calculated using the p-level effective action differ from the continuum limit by a term of order 1/N{sup p}. We obtain explicit expressions for the effective actions for levels p{<=}9. We end by analyzing the speedup of Monte Carlo simulations of two different models: an anharmonic oscillator with quartic coupling and a particle in a modified Poeschl-Teller potential.
A New Perspective on Path Integral Quantum Mechanics in Curved Space-Time
NASA Astrophysics Data System (ADS)
Singh, Dinesh; Mobed, Nader
2013-09-01
Abstract. A new approach to path integral quantum mechanics in curved space-time is presented for scalar particle propagation, expressed in terms of Lie transport and Fermi or Riemann normal co-ordinates to describe local curvature. While the presence of local curvature results in a strictly non-unitary representation of local time translation, the formalism nevertheless correctly recovers the free-particle Lagrangian in curved space-time, along with new terms that predict a simultaneous breakdown of time-reversal symmetry and a quantum violation of the weak equivalence principle at the particle's Compton wavelength scale. Furthermore, the formalism reveals the prediction of a gauge-invariant phase factor interpreted as the gravitational Aharonov-Bohm effect and Berry's phase.
Path-integral action of a particle in the noncommutative plane.
Gangopadhyay, Sunandan; Scholtz, Frederik G
2009-06-19
Noncommutative quantum mechanics can be viewed as a quantum system represented in the space of Hilbert-Schmidt operators acting on noncommutative configuration space. Taking this as a departure point, we formulate a coherent state approach to the path-integral representation of the transition amplitude. From this we derive an action for a particle moving in the noncommutative plane and in the presence of an arbitrary potential. We find that this action is nonlocal in time. However, this nonlocality can be removed by introducing an auxilary field, which leads to a second class constrained system that yields the noncommutative Heisenberg algebra upon quantization. Using this action, the propagator of the free particle and harmonic oscillator are computed explicitly.
Unified path integral treatment for generalized Hulthen and Woods-Saxon potentials
Benamira, F.; Guechi, L. . E-mail: Guechilarbi@yahoo.fr; Mameri, S.; Sadoun, M.A.
2007-09-15
A rigorous path integral discussion of the s states for a diatomic molecule potential with varying shape, which generalizes the Hulthen and the Woods-Saxon potentials, is presented. A closed form of the Green's function is obtained for different shapes of this potential. For {lambda}>=1 and (1/{eta})ln{lambda}
Topics in mode conversion theory and the group theoretical foundations of path integrals
NASA Astrophysics Data System (ADS)
Richardson, Andrew Stephen
discrete Beisenberg-Wey1 group to construct the symbol of a matrix. We then go on to show how the path integral arises when calculating the symbol of a function of an operator. We also show how the phase space and configuration space path integrals arise when considering reductions of the regular representation of the Heisenberg-Wey1 group to the primary representations and irreducible representations, respectively. We also show how the path integral can be interpreted as a Fourier transform on the space of measures, opening up the possibility of using tools from statistical mechanics (such as maximum entropy techniques) to analyze the path integral. We conclude with a survey of ideas for future research and describe several potential applications of this group theoretical perspective to problems in mode conversion.
NASA Astrophysics Data System (ADS)
Yoshikawa, Takehiro; Sugawara, Shuichi; Takayanagi, Toshiyuki; Shiga, Motoyuki; Tachikawa, Masanori
2012-02-01
Path-integral molecular dynamics simulations have been performed for porphycene and its isotopic variants in order to understand the effect of isotopic substitution of inner protons on the double proton transfer mechanism. We have used an on-the-fly direct dynamics technique at the semiempirical PM6 level combined with specific reaction parameterization. Our quantum simulations show that double proton transfer of the unsubstituted porphycene at T = 300 K mainly occurs via a so-called concerted mechanism through the D2h second-order saddle point. In addition, we found that both isotopic substitution and temperature significantly affect the double proton transfer mechanism. For example, the contribution of the stepwise mechanism increases with a temperature increase. We have also carried out hypothetical simulations with the porphycene configurations being completely planar. It has been found that out-of-plane vibrational motions significantly decrease the contribution of the concerted proton transfer mechanism.
NASA Astrophysics Data System (ADS)
Witt, Alexander; Ivanov, Sergei D.; Shiga, Motoyuki; Forbert, Harald; Marx, Dominik
2009-05-01
Centroid molecular dynamics (CMD) and ring polymer molecular dynamics (RPMD) are two conceptually distinct extensions of path integral molecular dynamics that are able to generate approximate quantum dynamics of complex molecular systems. Both methods can be used to compute quasiclassical time correlation functions which have direct application in molecular spectroscopy; in particular, to infrared spectroscopy via dipole autocorrelation functions. The performance of both methods for computing vibrational spectra of several simple but representative molecular model systems is investigated systematically as a function of temperature and isotopic substitution. In this context both CMD and RPMD feature intrinsic problems which are quantified and investigated in detail. Based on the obtained results guidelines for using CMD and RPMD to compute infrared spectra of molecular systems are provided.
NASA Astrophysics Data System (ADS)
Wang, Qi; Suzuki, Kimichi; Nagashima, Umpei; Tachikawa, Masanori; Yan, Shiwei
2013-11-01
The geometric isotope effects on the structures of hydrated chloride ionic hydrogen bonded clusters are explored by carrying out path integral molecular dynamics simulations. First, an outer shell coordinate is selected to display the rearrangement of single and multi hydration shell cluster structures. Next, to show the competition of intramolecular and intermolecular nuclear quantum effects, the intramolecular OH∗ stretching and intermolecular ion-water wagging motions are studied for single and multi shell structures, respectively. The results indicate that the intermolecular nuclear quantum effects stabilize the ionic hydrogen bonds in single shell structures, while they are destabilized through the competition with intramolecular nuclear quantum effects in multi shell structures. In addition, the correlations between ion-water stretching motion and other cluster vibrational coordinates are discussed. The results indicate that the intermolecular nuclear quantum effects on the cluster structures are strongly related to the cooperation of the water-water hydrogen bond interactions.
NASA Astrophysics Data System (ADS)
Reilly, Anthony M.; Habershon, Scott; Morrison, Carole A.; Rankin, David W. H.
2010-03-01
Path-integral molecular dynamics (PIMD) simulations with an empirical interaction potential have been used to determine the experimental equilibrium structure of solid nitromethane at 4.2 and 15 K. By comparing the time-averaged molecular structure determined in a PIMD simulation to the calculated minimum-energy (zero-temperature) molecular structure, we have derived structural corrections that describe the effects of thermal motion. These corrections were subsequently used to determine the equilibrium structure of nitromethane from the experimental time-averaged structure. We find that the corrections to the intramolecular and intermolecular bond distances, as well as to the torsion angles, are quite significant, particularly for those atoms participating in the anharmonic motion of the methyl group. Our results demonstrate that simple harmonic models of thermal motion may not be sufficiently accurate, even at low temperatures, while molecular simulations employing more realistic potential-energy surfaces can provide important insight into the role and magnitude of anharmonic atomic motions.
NASA Astrophysics Data System (ADS)
Ananth, Nandini
2013-09-01
We introduce mapping-variable ring polymer molecular dynamics (MV-RPMD), a model dynamics for the direct simulation of multi-electron processes. An extension of the RPMD idea, this method is based on an exact, imaginary time path-integral representation of the quantum Boltzmann operator using continuous Cartesian variables for both electronic states and nuclear degrees of freedom. We demonstrate the accuracy of the MV-RPMD approach in calculations of real-time, thermal correlation functions for a range of two-state single-mode model systems with different coupling strengths and asymmetries. Further, we show that the ensemble of classical trajectories employed in these simulations preserves the Boltzmann distribution and provides a direct probe into real-time coupling between electronic state transitions and nuclear dynamics.
Low-temperature metallic liquid hydrogen: an ab-initio path-integral molecular dynamics perspective
NASA Astrophysics Data System (ADS)
Chen, Ji; Li, Xin-Zheng; Zhang, Qianfan; Probert, Matthew; Pickard, Chris; Needs, Richard; Michaelides, Angelos; Wang, Enge
2013-03-01
Experiments and computer simulations have shown that the melting temperature of solid hydrogen drops with pressure above about 65 GPa, suggesting that a low temperature liquid state might exist. It has also been suggested that this liquid state might be non-molecular and metallic, although evidence for such behaviour is lacking. Using a combination of ab initio path-integral molecular dynamics and the two-phase methods, we have simulated the melting of solid hydrogen under finite temperatures. We found an atomic solid phase from 500 to 800 GPa which melts at < 200 K. Beyond this and up to pressures of 1,200 GPa a metallic atomic liquid is stable at temperatures as low as 50 K. The quantum motion of the protons is critical to the low melting temperature in this system as ab initio simulations with classical nuclei lead to a considerably higher melting temperature of ~300 K across the entire pressure range considered.
Hydrogen and muonium in diamond: A path-integral molecular dynamics simulation
NASA Astrophysics Data System (ADS)
Herrero, Carlos P.; Ramírez, Rafael; Hernández, Eduardo R.
2006-06-01
Isolated hydrogen, deuterium, and muonium in diamond have been studied by path-integral molecular dynamics simulations in the canonical ensemble. Finite-temperature properties of these point defects were analyzed in the range from 100 to 800K . Interatomic interactions were modeled by a tight-binding potential fitted to density-functional calculations. The most stable position for these hydrogenic impurities is found at the C-C bond center. Vibrational frequencies have been obtained from a linear-response approach, based on correlations of atom displacements at finite temperatures. The results show a large anharmonic effect in impurity vibrations at the bond center site, which hardens the vibrational modes with respect to a harmonic approximation. Zero-point motion causes an appreciable shift of the defect level in the electronic gap, as a consequence of electron-phonon interaction. This defect level goes down by 70meV when replacing hydrogen by muonium.
Low-temperature anharmonicity of barium titanate: A path-integral molecular-dynamics study
NASA Astrophysics Data System (ADS)
Geneste, Grégory; Dammak, Hichem; Hayoun, Marc; Thiercelin, Mickael
2013-01-01
We investigate the influence of quantum effects on the dielectric and piezoelectric properties of barium titanate in its (low-temperature) rhombohedral phase, and show the strongly anharmonic character of this system even at low temperature. For this purpose, we perform path-integral molecular-dynamics simulations under fixed pressure and fixed temperature, using an efficient Langevin thermostat-barostat, and an effective Hamiltonian derived from first-principles calculations. The quantum fluctuations are shown to significantly enhance the static dielectric susceptibility (≈ by a factor of 2) and the piezoelectric constants, reflecting the strong anharmonicity of this ferroelectric system even at very low temperature. The slow temperature-evolution of the dielectric properties observed below ≈100 K is attributed (i) to zero-point energy contributions and (ii) to harmonic behavior if the quantum effects are turned off.
Isotope effects in water as investigated by neutron diffraction and path integral molecular dynamics
NASA Astrophysics Data System (ADS)
Zeidler, Anita; Salmon, Philip S.; Fischer, Henry E.; Neuefeind, Jörg C.; Simonson, J. Mike; Markland, Thomas E.
2012-07-01
The structures of heavy and light water at 300 K were investigated by using a joint approach in which the method of neutron diffraction with oxygen isotope substitution was complemented by path integral molecular dynamics simulations. The diffraction results, which give intra-molecular O-D and O-H bond distances of 0.985(5) and 0.990(5) Å, were found to be in best agreement with those obtained by using the flexible anharmonic TTM3-F water model. Both techniques show a difference of ≃ 0.5% between the O-D and O-H intra-molecular bond lengths, and the results support a competing quantum effects model for water in which its structural and dynamical properties are governed by an offset between intra-molecular and inter-molecular quantum contributions. Further consideration of the O-O correlations is needed in order to improve agreement with experiment.
Path Integral Monte Carlo and Density Functional Molecular Dynamics Simulations of Warm Dense Matter
NASA Astrophysics Data System (ADS)
Militzer, Burkhard; Driver, Kevin
2011-10-01
We analyze the applicability of two first-principles simulation techniques, path integral Monte Carlo (PIMC) and density functional molecular dynamics (DFT-MD), to study the regime of warm dense matter. We discuss the advantages as well as the limitations of each method and propose directions for future development. Results for dense, liquid helium, where both methods have been applied, demonstrate the range of each method's applicability. Comparison of the equations of state from simulations with analytical theories and free energy models show that DFT is useful for temperatures below 100000 K and then PIMC provides accurate results for all higher temperatures. We characterize the structure of the liquid in terms of pair correlation functions and study the closure of the band gap with increasing density and temperature. Finally, we discuss simulations of heavier elements and demonstrate the reliability are both methods in such cases with preliminary results.
NASA Technical Reports Server (NTRS)
Singh, Upendra N.; Yu, Jirong; Petros, Mulugeta; Refaat, Tamer F.; Remus, Ruben G.; Fay, James J.; Reithmaier, Karl
2014-01-01
Double-pulse 2-micron lasers have been demonstrated with energy as high as 600 millijouls and up to 10 Hz repetition rate. The two laser pulses are separated by 200 microseconds and can be tuned and locked separately. Applying double-pulse laser in DIAL system enhances the CO2 measurement capability by increasing the overlap of the sampled volume between the on-line and off-line. To avoid detection complicity, integrated path differential absorption (IPDA) lidar provides higher signal-to-noise ratio measurement compared to conventional range-resolved DIAL. Rather than weak atmospheric scattering returns, IPDA rely on the much stronger hard target returns that is best suited for airborne platforms. In addition, the IPDA technique measures the total integrated column content from the instrument to the hard target but with weighting that can be tuned by the transmitter. Therefore, the transmitter could be tuned to weight the column measurement to the surface for optimum CO2 interaction studies or up to the free troposphere for optimum transport studies. Currently, NASA LaRC is developing and integrating a double-Pulsed 2-micron direct detection IPDA lidar for CO2 column measurement from an airborne platform. The presentation will describe the development of the 2-micron IPDA lidar system and present the airborne measurement of column CO2 and will compare to in-situ measurement for various ground target of different reflectivity.
NASA Astrophysics Data System (ADS)
Singh, Upendra N.; Yu, Jirong; Petros, Mulugeta; Refaat, Tamer F.; Remus, Ruben G.; Fay, James J.; Reithmaier, Karl
2014-10-01
Double-pulse 2-micron lasers have been demonstrated with energy as high as 600 mJ and up to 10 Hz repetition rate. The two laser pulses are separated by 200 µs and can be tuned and locked separately. Applying double-pulse laser in DIAL system enhances the CO2 measurement capability by increasing the overlap of the sampled volume between the on-line and off-line. To avoid detection complicity, integrated path differential absorption (IPDA) lidar provides higher signal-to-noise ratio measurement compared to conventional range-resolved DIAL. Rather than weak atmospheric scattering returns, IPDA rely on the much stronger hard target returns that is best suited for airborne platforms. In addition, the IPDA technique measures the total integrated column content from the instrument to the hard target but with weighting that can be tuned by the transmitter. Therefore, the transmitter could be tuned to weight the column measurement to the surface for optimum CO2 interaction studies or up to the free troposphere for optimum transport studies. Currently, NASA LaRC is developing and integrating a double-Pulsed 2-µm direct detection IPDA lidar for CO2 column measurement from an airborne platform. The presentation will describe the development of the 2-μm IPDA lidar system and present the airborne measurement of column CO2 and will compare to in-situ measurement for various ground target of different reflectivity.
Fermionic path-integral Monte Carlo results for the uniform electron gas at finite temperature.
Filinov, V S; Fortov, V E; Bonitz, M; Moldabekov, Zh
2015-03-01
The uniform electron gas (UEG) at finite temperature has recently attracted substantial interest due to the experimental progress in the field of warm dense matter. To explain the experimental data, accurate theoretical models for high-density plasmas are needed that depend crucially on the quality of the thermodynamic properties of the quantum degenerate nonideal electrons and of the treatment of their interaction with the positive background. Recent fixed-node path-integral Monte Carlo (RPIMC) data are believed to be the most accurate for the UEG at finite temperature, but they become questionable at high degeneracy when the Brueckner parameter rs=a/aB--the ratio of the mean interparticle distance to the Bohr radius--approaches 1. The validity range of these simulations and their predictive capabilities for the UEG are presently unknown. This is due to the unknown quality of the used fixed nodes and of the finite-size scaling from N=33 simulated particles (per spin projection) to the macroscopic limit. To analyze these questions, we present alternative direct fermionic path integral Monte Carlo (DPIMC) simulations that are independent from RPIMC. Our simulations take into account quantum effects not only in the electron system but also in their interaction with the uniform positive background. Also, we use substantially larger particle numbers (up to three times more) and perform an extrapolation to the macroscopic limit. We observe very good agreement with RPIMC, for the polarized electron gas, up to moderate densities around rs=4, and larger deviations for the unpolarized case, for low temperatures. For higher densities (high electron degeneracy), rs≲1.5, both RPIMC and DPIMC are problematic due to the increased fermion sign problem.
Maintaining a Cognitive Map in Darkness: The Need to Fuse Boundary Knowledge with Path Integration
Cheung, Allen; Ball, David; Milford, Michael; Wyeth, Gordon; Wiles, Janet
2012-01-01
Spatial navigation requires the processing of complex, disparate and often ambiguous sensory data. The neurocomputations underpinning this vital ability remain poorly understood. Controversy remains as to whether multimodal sensory information must be combined into a unified representation, consistent with Tolman's “cognitive map”, or whether differential activation of independent navigation modules suffice to explain observed navigation behaviour. Here we demonstrate that key neural correlates of spatial navigation in darkness cannot be explained if the path integration system acted independently of boundary (landmark) information. In vivo recordings demonstrate that the rodent head direction (HD) system becomes unstable within three minutes without vision. In contrast, rodents maintain stable place fields and grid fields for over half an hour without vision. Using a simple HD error model, we show analytically that idiothetic path integration (iPI) alone cannot be used to maintain any stable place representation beyond two to three minutes. We then use a measure of place stability based on information theoretic principles to prove that featureless boundaries alone cannot be used to improve localization above chance level. Having shown that neither iPI nor boundaries alone are sufficient, we then address the question of whether their combination is sufficient and – we conjecture – necessary to maintain place stability for prolonged periods without vision. We addressed this question in simulations and robot experiments using a navigation model comprising of a particle filter and boundary map. The model replicates published experimental results on place field and grid field stability without vision, and makes testable predictions including place field splitting and grid field rescaling if the true arena geometry differs from the acquired boundary map. We discuss our findings in light of current theories of animal navigation and neuronal computation, and
A transformed path integral approach for solution of the Fokker-Planck equation
NASA Astrophysics Data System (ADS)
Subramaniam, Gnana M.; Vedula, Prakash
2017-10-01
A novel path integral (PI) based method for solution of the Fokker-Planck equation is presented. The proposed method, termed the transformed path integral (TPI) method, utilizes a new formulation for the underlying short-time propagator to perform the evolution of the probability density function (PDF) in a transformed computational domain where a more accurate representation of the PDF can be ensured. The new formulation, based on a dynamic transformation of the original state space with the statistics of the PDF as parameters, preserves the non-negativity of the PDF and incorporates short-time properties of the underlying stochastic process. New update equations for the state PDF in a transformed space and the parameters of the transformation (including mean and covariance) that better accommodate nonlinearities in drift and non-Gaussian behavior in distributions are proposed (based on properties of the SDE). Owing to the choice of transformation considered, the proposed method maps a fixed grid in transformed space to a dynamically adaptive grid in the original state space. The TPI method, in contrast to conventional methods such as Monte Carlo simulations and fixed grid approaches, is able to better represent the distributions (especially the tail information) and better address challenges in processes with large diffusion, large drift and large concentration of PDF. Additionally, in the proposed TPI method, error bounds on the probability in the computational domain can be obtained using the Chebyshev's inequality. The benefits of the TPI method over conventional methods are illustrated through simulations of linear and nonlinear drift processes in one-dimensional and multidimensional state spaces. The effects of spatial and temporal grid resolutions as well as that of the diffusion coefficient on the error in the PDF are also characterized.
Maintaining a cognitive map in darkness: the need to fuse boundary knowledge with path integration.
Cheung, Allen; Ball, David; Milford, Michael; Wyeth, Gordon; Wiles, Janet
2012-01-01
Spatial navigation requires the processing of complex, disparate and often ambiguous sensory data. The neurocomputations underpinning this vital ability remain poorly understood. Controversy remains as to whether multimodal sensory information must be combined into a unified representation, consistent with Tolman's "cognitive map", or whether differential activation of independent navigation modules suffice to explain observed navigation behaviour. Here we demonstrate that key neural correlates of spatial navigation in darkness cannot be explained if the path integration system acted independently of boundary (landmark) information. In vivo recordings demonstrate that the rodent head direction (HD) system becomes unstable within three minutes without vision. In contrast, rodents maintain stable place fields and grid fields for over half an hour without vision. Using a simple HD error model, we show analytically that idiothetic path integration (iPI) alone cannot be used to maintain any stable place representation beyond two to three minutes. We then use a measure of place stability based on information theoretic principles to prove that featureless boundaries alone cannot be used to improve localization above chance level. Having shown that neither iPI nor boundaries alone are sufficient, we then address the question of whether their combination is sufficient and--we conjecture--necessary to maintain place stability for prolonged periods without vision. We addressed this question in simulations and robot experiments using a navigation model comprising of a particle filter and boundary map. The model replicates published experimental results on place field and grid field stability without vision, and makes testable predictions including place field splitting and grid field rescaling if the true arena geometry differs from the acquired boundary map. We discuss our findings in light of current theories of animal navigation and neuronal computation, and elaborate on
Herring, Nicole R.; Schaefer, Tori L.; Gudelsky, Gary A.; Vorhees, Charles V.; Williams, Michael T.
2008-01-01
Rationale Methamphetamine (MA) has been implicated in cognitive deficits in humans after chronic use. Animal models of neurotoxic MA exposure reveal persistent damage to monoaminergic systems, but few associated cognitive effects. Objectives Since, questions have been raised about the typical neurotoxic dosing regimen used in animals and whether it adequately models human cumulative drug exposure, these experiments examined two different dosing regimens. Methods Rats were treated with one of two regimens, one the typical neurotoxic regimen (4 × 10 mg/kg every 2 h) and one based on pharmacokinetic modeling (Cho et al. 2001) designed to better represent accumulating plasma concentrations of MA as seen in human users (24 ×1.67 mg/kg once every 15 min); matched for total daily dose. In two separate experiments, dosing regimens were compared for their effects on markers of neurotoxicity or on behavior. Results On markers of neurotoxicity, MA showed decreased DA and 5-HT, and increased glial fibrillary acidic protein and increased corticosterone levels regardless of dosing regimen 3 days post-treatment. Behaviorally, MA-treated groups, regardless of dosing regimen, showed hypoactivity, increased initial hyperactivity to a subsequent MA challenge, impaired novel object recognition, impaired learning in a multiple-T water maze test of path integration, and no differences on spatial navigation or reference memory in the Morris water maze. After behavioral testing, reductions of DA and 5-HT remained. Conclusions MA treatment induces an effect on path integration learning not previously reported. Dosing regimen had no differential effects on behavior or neurotoxicity. PMID:18509623
Fine, Dana S.; Sawin, Stephen
2014-06-15
Following Feynman's prescription for constructing a path integral representation of the propagator of a quantum theory, a short-time approximation to the propagator for imaginary-time, N = 1 supersymmetric quantum mechanics on a compact, even-dimensional Riemannian manifold is constructed. The path integral is interpreted as the limit of products, determined by a partition of a finite time interval, of this approximate propagator. The limit under refinements of the partition is shown to converge uniformly to the heat kernel for the Laplace-de Rham operator on forms. A version of the steepest descent approximation to the path integral is obtained, and shown to give the expected short-time behavior of the supertrace of the heat kernel.
Song, Linze; Shi, Qiang
2015-05-07
We present a new non-perturbative method to calculate the charge carrier mobility using the imaginary time path integral approach, which is based on the Kubo formula for the conductivity, and a saddle point approximation to perform the analytic continuation. The new method is first tested using a benchmark calculation from the numerical exact hierarchical equations of motion method. Imaginary time path integral Monte Carlo simulations are then performed to explore the temperature dependence of charge carrier delocalization and mobility in organic molecular crystals (OMCs) within the Holstein and Holstein-Peierls models. The effects of nonlocal electron-phonon interaction on mobility in different charge transport regimes are also investigated.
Song, Linze; Shi, Qiang
2015-05-07
We present a new non-perturbative method to calculate the charge carrier mobility using the imaginary time path integral approach, which is based on the Kubo formula for the conductivity, and a saddle point approximation to perform the analytic continuation. The new method is first tested using a benchmark calculation from the numerical exact hierarchical equations of motion method. Imaginary time path integral Monte Carlo simulations are then performed to explore the temperature dependence of charge carrier delocalization and mobility in organic molecular crystals (OMCs) within the Holstein and Holstein-Peierls models. The effects of nonlocal electron-phonon interaction on mobility in different charge transport regimes are also investigated.
Causo, Maria Serena; Ciccotti, Giovanni; Montemayor, Daniel; Bonella, Sara; Coker, David F
2005-04-14
We generalize the linearized path integral approach to evaluate quantum time correlation functions for systems best described by a set of nuclear and electronic degrees of freedom, restricting ourselves to the adiabatic approximation. If the operators in the correlation function are nondiagonal in the electronic states, then this adiabatic linearized path integral approximation for the thermal averaged quantum dynamics presents interesting and distinctive features, which we derive and explore in this paper. The capability of these approximations to accurately reproduce the behavior of physical systems is demonstrated by calculating the diffusion constant for an excess electron in a metal-molten salt solution.
Walters, D M; Stringer, S M
2010-07-01
A key question in understanding the neural basis of path integration is how individual, spatially responsive, neurons may self-organize into networks that can, through learning, integrate velocity signals to update a continuous representation of location within an environment. It is of vital importance that this internal representation of position is updated at the correct speed, and in real time, to accurately reflect the motion of the animal. In this article, we present a biologically plausible model of velocity path integration of head direction that can solve this problem using neuronal time constants to effect natural time delays, over which associations can be learned through associative Hebbian learning rules. The model comprises a linked continuous attractor network and competitive network. In simulation, we show that the same model is able to learn two different speeds of rotation when implemented with two different values for the time constant, and without the need to alter any other model parameters. The proposed model could be extended to path integration of place in the environment, and path integration of spatial view.
NASA Technical Reports Server (NTRS)
Singh, Upendra N.; Refaat, Tamer F.; Petros, Mulugeta; Yu, Jirong
2015-01-01
The two-micron wavelength is suitable for monitoring atmospheric water vapor and carbon dioxide, the two most dominant greenhouse gases. Recent advances in 2-micron laser technology paved the way for constructing state-of-the-art lidar transmitters for active remote sensing applications. In this paper, a new triple-pulsed 2-micron integrated path differential absorption lidar is presented. This lidar is capable of measuring either two species or single specie with two different weighting functions, simultaneously and independently. Development of this instrument is conducted at NASA Langley Research Center. Instrument scaling for projected future space missions will be discussed.
PathText: a text mining integrator for biological pathway visualizations
Kemper, Brian; Matsuzaki, Takuya; Matsuoka, Yukiko; Tsuruoka, Yoshimasa; Kitano, Hiroaki; Ananiadou, Sophia; Tsujii, Jun'ichi
2010-01-01
Motivation: Metabolic and signaling pathways are an increasingly important part of organizing knowledge in systems biology. They serve to integrate collective interpretations of facts scattered throughout literature. Biologists construct a pathway by reading a large number of articles and interpreting them as a consistent network, but most of the models constructed currently lack direct links to those articles. Biologists who want to check the original articles have to spend substantial amounts of time to collect relevant articles and identify the sections relevant to the pathway. Furthermore, with the scientific literature expanding by several thousand papers per week, keeping a model relevant requires a continuous curation effort. In this article, we present a system designed to integrate a pathway visualizer, text mining systems and annotation tools into a seamless environment. This will enable biologists to freely move between parts of a pathway and relevant sections of articles, as well as identify relevant papers from large text bases. The system, PathText, is developed by Systems Biology Institute, Okinawa Institute of Science and Technology, National Centre for Text Mining (University of Manchester) and the University of Tokyo, and is being used by groups of biologists from these locations. Contact: brian@monrovian.com. PMID:20529930
Ab initio path-integral molecular dynamics and the quantum nature of hydrogen bonds
NASA Astrophysics Data System (ADS)
Yexin, Feng; Ji, Chen; Xin-Zheng, Li; Enge, Wang
2016-01-01
The hydrogen bond (HB) is an important type of intermolecular interaction, which is generally weak, ubiquitous, and essential to life on earth. The small mass of hydrogen means that many properties of HBs are quantum mechanical in nature. In recent years, because of the development of computer simulation methods and computational power, the influence of nuclear quantum effects (NQEs) on the structural and energetic properties of some hydrogen bonded systems has been intensively studied. Here, we present a review of these studies by focussing on the explanation of the principles underlying the simulation methods, i.e., the ab initio path-integral molecular dynamics. Its extension in combination with the thermodynamic integration method for the calculation of free energies will also be introduced. We use two examples to show how this influence of NQEs in realistic systems is simulated in practice. Project supported by the National Natural Science Foundation of China (Grant Nos. 11275008, 91021007, and 10974012) and the China Postdoctoral Science Foundation (Grant No. 2014M550005).
PathText: a text mining integrator for biological pathway visualizations.
Kemper, Brian; Matsuzaki, Takuya; Matsuoka, Yukiko; Tsuruoka, Yoshimasa; Kitano, Hiroaki; Ananiadou, Sophia; Tsujii, Jun'ichi
2010-06-15
Metabolic and signaling pathways are an increasingly important part of organizing knowledge in systems biology. They serve to integrate collective interpretations of facts scattered throughout literature. Biologists construct a pathway by reading a large number of articles and interpreting them as a consistent network, but most of the models constructed currently lack direct links to those articles. Biologists who want to check the original articles have to spend substantial amounts of time to collect relevant articles and identify the sections relevant to the pathway. Furthermore, with the scientific literature expanding by several thousand papers per week, keeping a model relevant requires a continuous curation effort. In this article, we present a system designed to integrate a pathway visualizer, text mining systems and annotation tools into a seamless environment. This will enable biologists to freely move between parts of a pathway and relevant sections of articles, as well as identify relevant papers from large text bases. The system, PathText, is developed by Systems Biology Institute, Okinawa Institute of Science and Technology, National Centre for Text Mining (University of Manchester) and the University of Tokyo, and is being used by groups of biologists from these locations.
NASA Astrophysics Data System (ADS)
Fishman, Louis
2000-11-01
The role of mathematical modeling in the physical sciences will be briefly addressed. Examples will focus on computational acoustics, with applications to underwater sound propagation, electromagnetic modeling, optics, and seismic inversion. Direct and inverse wave propagation problems in both the time and frequency domains will be considered. Focusing on fixed-frequency (elliptic) wave propagation problems, the usual, two-way, partial differential equation formulation will be exactly reformulated, in a well-posed manner, as a one-way (marching) problem. This is advantageous for both direct and inverse considerations, as well as stochastic modeling problems. The reformulation will require the introduction of pseudodifferential operators and their accompanying phase space analysis (calculus), in addition to path integral representations for the fundamental solutions and their subsequent computational algorithms. Unlike the more traditional, purely numerical applications of, for example, finite-difference and finite-element methods, this approach, in effect, writes the exact, or, more generally, the asymptotically correct, answer as a functional integral and, subsequently, computes it directly. The overall computational philosophy is to combine analysis, asymptotics, and numerical methods to attack complicated, real-world problems. Exact and asymptotic analysis will stress the complementary nature of the direct and inverse formulations, as well as indicating the explicit structural connections between the time- and frequency-domain solutions.
Semi-classical Locality for the Non-relativistic Path Integral in Configuration Space
NASA Astrophysics Data System (ADS)
Gomes, Henrique
2017-09-01
In an accompanying paper Gomes (arXiv:1504.02818, 2015), we have put forward an interpretation of quantum mechanics based on a non-relativistic, Lagrangian 3+1 formalism of a closed Universe M, existing on timeless configuration space Q of some field over M. However, not much was said there about the role of locality, which was not assumed. This paper is an attempt to fill that gap. Locality in full can only emerge dynamically, and is not postulated. This new understanding of locality is based solely on the properties of extremal paths in configuration space. I do not demand locality from the start, as it is usually done, but showed conditions under which certain systems exhibit it spontaneously. In this way we recover semi-classical local behavior when regions dynamically decouple from each other, a notion more appropriate for extension into quantum mechanics. The dynamics of a sub-region O within the closed manifold M is independent of its complement, M-O, if the projection of extremal curves on Q onto the space of extremal curves intrinsic to O is a surjective map. This roughly corresponds to e^{i\\hat{H}t}circ prO= prOcirc e^{i\\hat{H}t}, where prO:Q→ Q_O^{partial O} is a linear projection. This criterion for locality can be made approximate—an impossible feat had it been already postulated—and it can be applied for theories which do not have hyperbolic equations of motion, and/or no fixed causal structure. When two regions are mutually independent according to the criterion proposed here, the semi-classical path integral kernel factorizes, showing cluster decomposition which is the ultimate aim of a definition of locality.
Semi-classical Locality for the Non-relativistic Path Integral in Configuration Space
NASA Astrophysics Data System (ADS)
Gomes, Henrique
2017-06-01
In an accompanying paper Gomes (arXiv:1504.02818, 2015), we have put forward an interpretation of quantum mechanics based on a non-relativistic, Lagrangian 3+1 formalism of a closed Universe M, existing on timeless configuration space Q of some field over M. However, not much was said there about the role of locality, which was not assumed. This paper is an attempt to fill that gap. Locality in full can only emerge dynamically, and is not postulated. This new understanding of locality is based solely on the properties of extremal paths in configuration space. I do not demand locality from the start, as it is usually done, but showed conditions under which certain systems exhibit it spontaneously. In this way we recover semi-classical local behavior when regions dynamically decouple from each other, a notion more appropriate for extension into quantum mechanics. The dynamics of a sub-region O within the closed manifold M is independent of its complement, M-O , if the projection of extremal curves on Q onto the space of extremal curves intrinsic to O is a surjective map. This roughly corresponds to e^{i\\hat{H}t}° prO= prO° e^{i\\hat{H}t} , where prO:Q→ Q_O^{partial O} is a linear projection. This criterion for locality can be made approximate—an impossible feat had it been already postulated—and it can be applied for theories which do not have hyperbolic equations of motion, and/or no fixed causal structure. When two regions are mutually independent according to the criterion proposed here, the semi-classical path integral kernel factorizes, showing cluster decomposition which is the ultimate aim of a definition of locality.
Wong, Kin-Yiu; Xu, Yuqing; Xu, Liang
2015-11-01
Enzymatic reactions are integral components in many biological functions and malfunctions. The iconic structure of each reaction path for elucidating the reaction mechanism in details is the molecular structure of the rate-limiting transition state (RLTS). But RLTS is very hard to get caught or to get visualized by experimentalists. In spite of the lack of explicit molecular structure of the RLTS in experiment, we still can trace out the RLTS unique "fingerprints" by measuring the isotope effects on the reaction rate. This set of "fingerprints" is considered as a most direct probe of RLTS. By contrast, for computer simulations, oftentimes molecular structures of a number of TS can be precisely visualized on computer screen, however, theoreticians are not sure which TS is the actual rate-limiting one. As a result, this is an excellent stage setting for a perfect "marriage" between experiment and theory for determining the structure of RLTS, along with the reaction mechanism, i.e., experimentalists are responsible for "fingerprinting", whereas theoreticians are responsible for providing candidates that match the "fingerprints". In this Review, the origin of isotope effects on a chemical reaction is discussed from the perspectives of classical and quantum worlds, respectively (e.g., the origins of the inverse kinetic isotope effects and all the equilibrium isotope effects are purely from quantum). The conventional Bigeleisen equation for isotope effect calculations, as well as its refined version in the framework of Feynman's path integral and Kleinert's variational perturbation (KP) theory for systematically incorporating anharmonicity and (non-parabolic) quantum tunneling, are also presented. In addition, the outstanding interplay between theory and experiment for successfully deducing the RLTS structures and the reaction mechanisms is demonstrated by applications on biochemical reactions, namely models of bacterial squalene-to-hopene polycyclization and RNA 2'-O
ERIC Educational Resources Information Center
Field, J. H.
2011-01-01
It is shown how the time-dependent Schrodinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equation of classical mechanics. Schrodinger's own published derivations of quantum wave equations, the first of which was also based on the Hamilton-Jacobi…
Bastatas, Lyndon D.; Bornales, Jinky B.
2008-06-18
White noise path integral prescription is applied to solve the Dirac equation for a two-dimensional Dirac oscillator in a uniform magnetic field. The energy spectrum obtained agrees with the result obtained by Villalba and Maggiolo using the differential approach.
ERIC Educational Resources Information Center
Field, J. H.
2011-01-01
It is shown how the time-dependent Schrodinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equation of classical mechanics. Schrodinger's own published derivations of quantum wave equations, the first of which was also based on the Hamilton-Jacobi…
Emissions of ammonia and methane from an anaerobic lagoon at a swine animal feeding operation were evaluated five times over a period of two years. The plane-integrated (PI) open-path Fourier transform infrared spectrometry (OP-FTIR) methodology was used to transect the plume at ...
ERIC Educational Resources Information Center
Miller, Melvin E., Ed.; Cook-Greuter, Susanne R., Ed.
This book contains 11 papers on creativity, spirituality, and transcendence as paths to integrity and wisdom in the mature self. The book begins with the paper "Introduction--Creativity in Adulthood: Personal Maturity and Openness to Extraordinary Sources of Inspiration" (Susanne R. Cook-Greuter, Melvin E. Miller). The next four papers,…
Page, Hector J I; Walters, Daniel; Stringer, Simon M
2015-01-01
Head direction cells fire to signal the direction in which an animal's head is pointing. They are able to track head direction using only internally-derived information (path integration)In this simulation study we investigate the factors that affect path integration accuracy. Specifically, two major limiting factors are identified: rise time, the time after stimulation it takes for a neuron to start firing, and the presence of symmetric non-offset within-layer recurrent collateral connectivity. On the basis of the latter, the important prediction is made that head direction cell regions directly involved in path integration will not contain this type of connectivity; giving a theoretical explanation for architectural observations. Increased neuronal rise time is found to slow path integration, and the slowing effect for a given rise time is found to be more severe in the context of short conduction delays. Further work is suggested on the basis of our findings, which represent a valuable contribution to understanding of the head direction cell system.
Page, Hector J. I.; Walters, Daniel; Stringer, Simon M.
2015-01-01
Head direction cells fire to signal the direction in which an animal's head is pointing. They are able to track head direction using only internally-derived information (path integration)In this simulation study we investigate the factors that affect path integration accuracy. Specifically, two major limiting factors are identified: rise time, the time after stimulation it takes for a neuron to start firing, and the presence of symmetric non-offset within-layer recurrent collateral connectivity. On the basis of the latter, the important prediction is made that head direction cell regions directly involved in path integration will not contain this type of connectivity; giving a theoretical explanation for architectural observations. Increased neuronal rise time is found to slow path integration, and the slowing effect for a given rise time is found to be more severe in the context of short conduction delays. Further work is suggested on the basis of our findings, which represent a valuable contribution to understanding of the head direction cell system. PMID:25705190
Grinberg, H.; Maranon, J.; Vucetich, H.
1983-01-15
The Kustaanheimo--Stiefel transformation together with the well-known expansion of the kernel of an isotropic harmonic oscillator is used to generate the atomic orbitals of the nonrelativistic hydrogen atom in a four-dimensional Riemann space through the path integral formalism. Group theoretical implications of the present problem are briefly discussed.
Emissions of ammonia and methane from an anaerobic lagoon at a swine animal feeding operation were evaluated five times over a period of two years. The plane-integrated (PI) open-path Fourier transform infrared spectrometry (OP-FTIR) methodology was used to transect the plume at ...
Botelho, L.C.L.
1985-03-15
We study a two-dimensional quantum field model with axial-vector-current--pseudoscalar derivative interaction using path-integral methods. We construct an effective Lagrangian by performing a chiral change in the fermionic variables leading to an exact solution of the model.
Kleinert, H; Zatloukal, V
2013-11-01
The statistics of rare events, the so-called black-swan events, is governed by non-Gaussian distributions with heavy power-like tails. We calculate the Green functions of the associated Fokker-Planck equations and solve the related stochastic differential equations. We also discuss the subject in the framework of path integration.
ERIC Educational Resources Information Center
Miller, Melvin E., Ed.; Cook-Greuter, Susanne R., Ed.
This book contains 11 papers on creativity, spirituality, and transcendence as paths to integrity and wisdom in the mature self. The book begins with the paper "Introduction--Creativity in Adulthood: Personal Maturity and Openness to Extraordinary Sources of Inspiration" (Susanne R. Cook-Greuter, Melvin E. Miller). The next four papers,…
NASA Astrophysics Data System (ADS)
Shiga, Motoyuki; Tachikawa, Masanori; Miura, Shinichi
2000-12-01
We present an accurate calculational scheme for many-body systems composed of electrons and nuclei, by path integral molecular dynamics technique combined with the ab initio molecular orbital theory. Based upon the scheme, the simulation of a water molecule at room temperature is demonstrated, applying all-electron calculation at the Hartree-Fock level of theory.
Wiese, Kay Jörg
2016-04-01
We derive and study two different formalisms used for nonequilibrium processes: the coherent-state path integral, and an effective, coarse-grained stochastic equation of motion. We first study the coherent-state path integral and the corresponding field theory, using the annihilation process A+A→A as an example. The field theory contains counterintuitive quartic vertices. We show how they can be interpreted in terms of a first-passage problem. Reformulating the coherent-state path integral as a stochastic equation of motion, the noise generically becomes imaginary. This renders it not only difficult to interpret, but leads to convergence problems at finite times. We then show how alternatively an effective coarse-grained stochastic equation of motion with real noise can be constructed. The procedure is similar in spirit to the derivation of the mean-field approximation for the Ising model, and the ensuing construction of its effective field theory. We finally apply our findings to stochastic Manna sandpiles. We show that the coherent-state path integral is inappropriate, or at least inconvenient. As an alternative, we derive and solve its mean-field approximation, which we then use to construct a coarse-grained stochastic equation of motion with real noise.
NASA Astrophysics Data System (ADS)
Sesé, Luis M.
This paper addresses several points of interest concerning the computation of the static structure factor of path-integral monatomic quantum fluids. First of all, the connection between the structure factor and the path-integral linear response pair radial correlation function is shown as its defining quantity by assuming a generalized Fermi's potential for the neutron- nuclei interactions, which is to be included in the general expression of the dynamic structure factor. Second, the possibilities of finding Ornstein-Zernike equations for full path-integral fluids, and also for the effective potential models of fluids derived from the path-integral formalism, are explored by working in the grand canonical ensemble. By so doing, the success and features for improvement of the weak-field approach used previously in this context of determining quantum static structure factors [SESE,L.M.,1996, Molec. Phys., 89, 1783; SESE, L.M., and LEDESMA,R., 1997, J. chem. Phys., 106, 1134] can be understood. New numerical applications are performed within this weak-field approach taking as probes the quantum hard-sphere fluid and dense fluid helium-4, the latter being described through LennardJones and Aziz-Slaman underlying interactions. The results show that the structure factors associated with the linear response and instantaneous path-integral pair radial correlation functions differ noticeably from each other with increasing quantum effects. In particular, the linear response description leads to more compressible fluids than the instantaneous one. Besides, the equality between the isothermal compressibilities fixed via the linear response and the quantum particle centre-of-gravity pair radial correlation functions does not hold beyond the situations that can be treated with the Gaussian Feynman-Hibbs effective potential picture. Comparison with experiment in the case of helium-4 (T = 4.2 K) reveals clearly that, under strong quantum conditions, an operative framework more
Moving to a Soft Path for Water: Integrated Research and Management Needs
NASA Astrophysics Data System (ADS)
Gleick, P. H.
2011-12-01
Water on Earth in its three fundamental phases is integral to the functioning, dynamics, and variability of the global climatological and biological support systems. From a purely scientific point of view, understanding the complexity of the hydrological cycle is of paramount interest and central to our understanding of other planetary geological, atmospheric, chemical, and physical processes. But water is more than that: water is key to economic, social, and political issues as well, including some of the core challenges of our time such central to issues of poverty, health, environmental sustainability, conflict, and economic prosperity. The more society seeks to solve these challenges, the more obvious it becomes that we must improve more than just our understanding of the fundamental science of the hydrological cycle and its links with related global processes; we must also improve our understanding of the complex social, economic, and structural challenges facing water managers and users. We must move to a different paradigm where water is managed in a far more integrated way - what I call the "soft path for water." Central to our basic science needs are (1) an expansion of the frequency and nature of the data we collect, (2) the development of systems for managing, sharing, and analyzing those data, and (3) improvements in our ability to model and forecast the hydrological cycle together with other climatological, geophysical, and biochemical systems. These improvements would lead to a far better understanding of the local, regional, and global details of the water balance on timescales from minutes to millennia. These needs are increasingly well understood in the research community and extensive efforts in these areas are underway under the auspices of national research centers, universities, and international scientific collaborations. But it is also becoming increasingly apparent that many of the current water challenges facing society are not going to be
A path-integral Monte Carlo study of a small cluster: The Ar trimer
NASA Astrophysics Data System (ADS)
Pérez de Tudela, R.; Márquez-Mijares, M.; González-Lezana, T.; Roncero, O.; Miret-Artés, S.; Delgado-Barrio, G.; Villarreal, P.
2010-06-01
The Ar3 system has been studied between T =0 K and T =40 K by means of a path-integral Monte Carlo (PIMC) method. The behavior of the average energy in terms of the temperature has been explained by comparison with results obtained with the thermal averaged rovibrational spectra estimated via: (i) a quantum mechanical method based on distributed Gaussian functions for the interparticle distances and (ii) an analytical model which precisely accounts for the participation of the dissociative continua Ar2+Ar and Ar+Ar+Ar. Beyond T ˜20 K, the system explores floppier configurations than the rigid equilateral geometry, as linear and Ar-Ar2-like arrangements, and fragmentates around T ˜40 K. A careful investigation of the specific heat in terms of a confining radius in the PIMC calculation seems to discard a proper phase transition as in larger clusters, in apparent contradiction with previous reports of precise values for a liquid-gas transition. The onset of this noticeable change in the dynamics of the trimer occurs, however, at a remarkably low value of the temperature in comparison with Arn systems formed with more Ar atoms. Quantum mechanical effects are found of relevance at T ≤15 K, with both energies and radial distributions obtained with a quantum PIMC deviating from the corresponding classical results, thus precluding exclusively classical approaches for a precise description of the system at this low temperature range.
Bayesian Uncertainty Quantification for Bond Energies and Mobilities Using Path Integral Analysis
Chang, Joshua C.; Fok, Pak-Wing; Chou, Tom
2015-01-01
Dynamic single-molecule force spectroscopy is often used to distort bonds. The resulting responses, in the form of rupture forces, work applied, and trajectories of displacements, are used to reconstruct bond potentials. Such approaches often rely on simple parameterizations of one-dimensional bond potentials, assumptions on equilibrium starting states, and/or large amounts of trajectory data. Parametric approaches typically fail at inferring complicated bond potentials with multiple minima, while piecewise estimation may not guarantee smooth results with the appropriate behavior at large distances. Existing techniques, particularly those based on work theorems, also do not address spatial variations in the diffusivity that may arise from spatially inhomogeneous coupling to other degrees of freedom in the macromolecule. To address these challenges, we develop a comprehensive empirical Bayesian approach that incorporates data and regularization terms directly into a path integral. All experimental and statistical parameters in our method are estimated directly from the data. Upon testing our method on simulated data, our regularized approach requires less data and allows simultaneous inference of both complex bond potentials and diffusivity profiles. Crucially, we show that the accuracy of the reconstructed bond potential is sensitive to the spatially varying diffusivity and accurate reconstruction can be expected only when both are simultaneously inferred. Moreover, after providing a means for self-consistently choosing regularization parameters from data, we derive posterior probability distributions, allowing for uncertainty quantification. PMID:26331254
Dopieralski, Przemyslaw; Perrin, Charles L; Latajka, Zdzislaw
2011-11-08
The issue of the symmetry of short, low-barrier hydrogen bonds in solution is addressed here with advanced ab initio simulations of a hydrogen maleate anion in different environments, starting with the isolated anion, going through two crystal structures (sodium and potassium salts), then to an aqueous solution, and finally in the presence of counterions. By Car-Parrinello and path integral molecular dynamics simulations, it is demonstrated that the position of the proton in the intramolecular hydrogen bond of an aqueous hydrogen maleate anion is entirely related to the solvation pattern around the oxygen atoms of the intramolecular hydrogen bond. In particular, this anion has an asymmetric hydrogen bond, with the proton always located on the oxygen atom that is less solvated, owing to the instantaneous solvation environment. Simulations of water solutions of hydrogen maleate ion with two different counterions, K(+) and Na(+), surprisingly show that the intramolecular hydrogen-bond potential in the case of the Na(+) salt is always asymmetric, regardless of the hydrogen bonds to water, whereas for the K(+) salt, the potential for H motion depends on the location of the K(+). It is proposed that repulsion by the larger and more hydrated K(+) is weaker than that by Na(+) and competitive with solvation by water.
NASA Astrophysics Data System (ADS)
Liu, Bing-Yi; Wang, Jun-Yang; Liu, Zhi-Shen
2014-11-01
Spaceborne integrated path differential absorption (IPDA) lidar is an active-detection system which is able to perform global CO2 measurement with high accuracy of 1ppmv at day and night over ground and clouds. To evaluate the detection performance of the system, simulation of the ground return signal and retrieval algorithm for CO2 concentration are presented in this paper. Ground return signals of spaceborne IPDA lidar under various ground surface reflectivity and atmospheric aerosol optical depths are simulated using given system parameters, standard atmosphere profiles and HITRAN database, which can be used as reference for determining system parameters. The simulated signals are further applied to the research on retrieval algorithm for CO2 concentration. The column-weighted dry air mixing ratio of CO2 denoted by XCO2 is obtained. As the deviations of XCO2 between the initial values for simulation and the results from retrieval algorithm are within the expected error ranges, it is proved that the simulation and retrieval algorithm are reliable.
NASA Astrophysics Data System (ADS)
Roldán, Édgar; Gupta, Shamik
2017-08-01
We study the dynamics of overdamped Brownian particles diffusing in conservative force fields and undergoing stochastic resetting to a given location at a generic space-dependent rate of resetting. We present a systematic approach involving path integrals and elements of renewal theory that allows us to derive analytical expressions for a variety of statistics of the dynamics such as (i) the propagator prior to first reset, (ii) the distribution of the first-reset time, and (iii) the spatial distribution of the particle at long times. We apply our approach to several representative and hitherto unexplored examples of resetting dynamics. A particularly interesting example for which we find analytical expressions for the statistics of resetting is that of a Brownian particle trapped in a harmonic potential with a rate of resetting that depends on the instantaneous energy of the particle. We find that using energy-dependent resetting processes is more effective in achieving spatial confinement of Brownian particles on a faster time scale than performing quenches of parameters of the harmonic potential.
Oscillator-interference models of path integration do not require theta oscillations.
Orchard, Jeff
2015-03-01
Navigation and path integration in rodents seems to involve place cells, grid cells, and theta oscillations (4-12 Hz) in the local field potential. Two main theories have been proposed to explain the neurological underpinnings of how these phenomena relate to navigation and to each other. Attractor network (AN) models revolve around the idea that local excitation and long-range inhibition connectivity can spontaneously generate grid-cell-like activity patterns. Oscillator interference (OI) models propose that spatial patterns of activity are caused by the interference patterns between neural oscillators. In rats, these oscillators have a frequency close to the theta frequency. Recent studies have shown that bats do not exhibit a theta cycle when they crawl, and yet they still have grid cells. This has been interpreted as a criticism of OI models. However, OI models do not require theta oscillations. We explain why the absence of theta oscillations does not contradict OI models and discuss how the two families of models might be distinguished experimentally.
A new approach to gravitational clustering: A path-integral formalism and large-N expansions
NASA Astrophysics Data System (ADS)
Valageas, P.
2004-07-01
We show that the formation of large-scale structures through gravitational instability in the expanding universe can be fully described through a path-integral formalism. We derive the action S[f] which gives the statistical weight associated with any phase-space distribution function f({x},{p},t). This action S describes both the average over the Gaussian initial conditions and the Vlasov-Poisson dynamics. Next, applying a standard method borrowed from field theory we generalize our problem to an N-field system and we look for an expansion over powers of 1/N. We describe three such methods and we derive the corresponding equations of motion at the lowest non-trivial order for the case of gravitational clustering. This yields a set of non-linear equations for the mean /line{f} and the two-point correlation G of the phase-space distribution f, as well as for the response function R. These systematic schemes match the usual perturbative expansion on quasi-linear scales but should also be able to treat the non-linear regime. Our approach can also be extended to non-Gaussian initial conditions and may serve as a basis for other tools borrowed from field theory. Appendix A is only available in electronic form at http://www.edpsciences.org
Path-integral simulation of ice VII: Pressure and temperature effects
NASA Astrophysics Data System (ADS)
Herrero, Carlos P.; Ramírez, Rafael
2015-11-01
The effects of pressure and temperature on structural and thermodynamic properties of ice VII have been studied by using path-integral molecular dynamics (PIMD) simulations. Temperatures between 25 and 450 K, as well as pressures up to 12 GPa were considered. Interatomic interactions were modeled by using the effective q-TIP4P/F potential for flexible water. We analyze the pressure dependence of the molar volume, bulk modulus, interatomic distances, kinetic energy, and atomic delocalization at various temperatures. Results of PIMD simulations are compared with those derived from a quasi-harmonic approximation (QHA) of vibrational modes, which helps to assess the importance of anharmonic effects, as well as the influence of the different modes on the properties of ice VII. The accuracy of the QHA for describing this high-pressure phase decreases for rising temperature, but this approximation becomes more reliable as pressure grows, since anharmonicity becomes less relevant. Comparisons with low-pressure cubic ice are presented.
NASA Astrophysics Data System (ADS)
Tachikawa, Masanori; Shiga, Motoyuki
2004-09-01
We have applied the ab initio path integral molecular dynamics simulation to study hydronium ion and its isotopes, which are the simplest systems for hydrated proton and deuteron. In this simulation, all the rotational and vibrational degrees of freedom are treated fully quantum mechanically, while the potential energies of the respective atomic configurations are calculated "on the fly" using ab initio quantum chemical approach. With the careful treatment of the ab initio electronic structure calculation by relevant choices in electron correlation level and basis set, this scheme is theoretically quite rigorous except for Born-Oppenheimer approximation. This accurate calculation allows a close insight into the structural shifts for the isotopes of hydronium ion by taking account of both quantum mechanical and thermal effects. In fact, the calculation is shown to be successful to quantitatively extract the geometrical isotope effect with respect to the Walden inversion. It is also shown that this leads to the isotope effect on the electronic structure as well as the thermochemical properties.
Exact path-integral evaluation of the heat distribution function of a trapped Brownian oscillator
NASA Astrophysics Data System (ADS)
Chatterjee, Debarati; Cherayil, Binny J.
2010-11-01
Using path integrals, we derive an exact expression—valid at all times t —for the distribution P(Q,t) of the heat fluctuations Q of a Brownian particle trapped in a stationary harmonic well. We find that P(Q,t) can be expressed in terms of a modified Bessel function of zeroth order that in the limit t→∞ exactly recovers the heat distribution function obtained recently by Imparato [Phys. Rev. E 76, 050101(R) (2007)]10.1103/PhysRevE.76.050101 from the approximate solution to a Fokker-Planck equation. This long-time result is in very good agreement with experimental measurements carried out by the same group on the heat effects produced by single micron-sized polystyrene beads in a stationary optical trap. An earlier exact calculation of the heat distribution function of a trapped particle moving at a constant speed v was carried out by van Zon and Cohen [Phys. Rev. E 69, 056121 (2004)]10.1103/PhysRevE.69.056121; however, this calculation does not provide an expression for P(Q,t) itself, but only its Fourier transform (which cannot be analytically inverted), nor can it be used to obtain P(Q,t) for the case v=0 .
Iterative quantum-classical path integral with dynamically consistent state hopping
Walters, Peter L.; Makri, Nancy
2016-01-28
We investigate the convergence of iterative quantum-classical path integral calculations in sluggish environments strongly coupled to a quantum system. The number of classical trajectories, thus the computational cost, grows rapidly (exponentially, unless filtering techniques are employed) with the memory length included in the calculation. We argue that the choice of the (single) trajectory branch during the time preceding the memory interval can significantly affect the memory length required for convergence. At short times, the trajectory branch associated with the reactant state improves convergence by eliminating spurious memory. We also introduce an instantaneous population-based probabilistic scheme which introduces state-to-state hops in the retained pre-memory trajectory branch, and which is designed to choose primarily the trajectory branch associated with the reactant at early times, but to favor the product state more as the reaction progresses to completion. Test calculations show that the dynamically consistent state hopping scheme leads to accelerated convergence and a dramatic reduction of computational effort.
Neural Network-Based Solutions for Stochastic Optimal Control Using Path Integrals.
Rajagopal, Karthikeyan; Balakrishnan, Sivasubramanya Nadar; Busemeyer, Jerome R
2017-03-01
In this paper, an offline approximate dynamic programming approach using neural networks is proposed for solving a class of finite horizon stochastic optimal control problems. There are two approaches available in the literature, one based on stochastic maximum principle (SMP) formalism and the other based on solving the stochastic Hamilton-Jacobi-Bellman (HJB) equation. However, in the presence of noise, the SMP formalism becomes complex and results in having to solve a couple of backward stochastic differential equations. Hence, current solution methodologies typically ignore the noise effect. On the other hand, the inclusion of noise in the HJB framework is very straightforward. Furthermore, the stochastic HJB equation of a control-affine nonlinear stochastic system with a quadratic control cost function and an arbitrary state cost function can be formulated as a path integral (PI) problem. However, due to curse of dimensionality, it might not be possible to utilize the PI formulation for obtaining comprehensive solutions over the entire operating domain. A neural network structure called the adaptive critic design paradigm is used to effectively handle this difficulty. In this paper, a novel adaptive critic approach using the PI formulation is proposed for solving stochastic optimal control problems. The potential of the algorithm is demonstrated through simulation results from a couple of benchmark problems.
Efficient real-time path integrals for non-Markovian spin-boson models
NASA Astrophysics Data System (ADS)
Strathearn, A.; Lovett, B. W.; Kirton, P.
2017-09-01
Strong coupling between a system and its environment leads to the emergence of non-Markovian dynamics, which cannot be described by a time-local master equation. One way to capture such dynamics is to use numerical real-time path integrals, where assuming a finite bath memory time enables manageable simulation scaling. However, by comparing to the exactly soluble independent boson model, we show that the presence of transient negative decay rates in the exact dynamics can result in simulations with unphysical exponential growth of density matrix elements when the finite memory approximation is used. We therefore reformulate this approximation in such a way that the exact dynamics are reproduced identically and then apply our new method to the spin-boson model with superohmic environmental coupling, commonly used to model phonon environments, but which cannot be solved exactly. Our new method allows us to easily access parameter regimes where we find revivals in population dynamics which are due to non-Markovian backflow of information from the bath to the system.
NASA Astrophysics Data System (ADS)
Sesé, Luis M.
2017-02-01
This work deals with the computation of the structure factors of quantum fluids under complex conditions involving substantial density fluctuations and/or large particle delocalization effects. The method is based on the combination of path-integral Monte Carlo (PIMC) simulations and the pair Ornstein-Zernike framework (OZ2). PIMC provides the radial correlation functions (centroid, instantaneous, and thermalized-continuous total linear response), which are used as data input to the OZ2 calculations that lead to their associated structure factors. To undertake this project normal liquid 4He and supercritical 3He are selected, studying conditions in the range (T = 4.2 K; 0.01886 <ρN/Å-3 < 0.02687). Full inter-comparison between the structure factors determined via both OZ2 and direct PIMC calculations is made. In addition, comparison with experimental data, including thermodynamic properties, is made wherever possible. The results establish that, even under severe thermodynamic and/or quantum fluctuation conditions, OZ2 remains in the quantum domain as a highly reliable and cost-effective framework to determine accurate structure factors, also allowing one to understand the related isotopic shifts in fluid He.
Path Integral Monte Carlo finite-temperature electronic structure of quantum dots
NASA Astrophysics Data System (ADS)
Leino, Markku; Rantala, Tapio T.
2003-03-01
Quantum Monte Carlo methods allow a straightforward procedure for evaluation of electronic structures with a proper treatment of electronic correlations. This can be done even at finite temperatures [1]. We apply the Path Integral Monte Carlo (PIMC) simulation method [2] for one and two electrons in a single and double quantum dots. With this approach we evaluate the electronic distributions and correlations, and finite temperature effects on those. Temperature increase broadens the one-electron distribution as expected. This effect is smaller for correlated electrons than for single ones. The simulated one and two electron distributions of a single and two coupled quantum dots are also compared to those from experiments and other theoretical (0 K) methods [3]. Computational capacity is found to become the limiting factor in simulations with increasing accuracy. This and other essential aspects of PIMC and its capability in this type of calculations are also discussed. [1] R.P. Feynman: Statistical Mechanics, Addison Wesley, 1972. [2] D.M. Ceperley, Rev.Mod.Phys. 67, 279 (1995). [3] M. Pi, A. Emperador and M. Barranco, Phys.Rev.B 63, 115316 (2001).
Continuum tensor network field states, path integral representations and spatial symmetries
NASA Astrophysics Data System (ADS)
Jennings, David; Brockt, Christoph; Haegeman, Jutho; Osborne, Tobias J.; Verstraete, Frank
2015-06-01
A natural way to generalize tensor network variational classes to quantum field systems is via a continuous tensor contraction. This approach is first illustrated for the class of quantum field states known as continuous matrix-product states (cMPS). As a simple example of the path-integral representation we show that the state of a dynamically evolving quantum field admits a natural representation as a cMPS. A completeness argument is also provided that shows that all states in Fock space admit a cMPS representation when the number of variational parameters tends to infinity. Beyond this, we obtain a well-behaved field limit of projected entangled-pair states (PEPS) in two dimensions that provide an abstract class of quantum field states with natural symmetries. We demonstrate how symmetries of the physical field state are encoded within the dynamics of an auxiliary field system of one dimension less. In particular, the imposition of Euclidean symmetries on the physical system requires that the auxiliary system involved in the class’ definition must be Lorentz-invariant. The physical field states automatically inherit entropy area laws from the PEPS class, and are fully described by the dissipative dynamics of a lower dimensional virtual field system. Our results lie at the intersection many-body physics, quantum field theory and quantum information theory, and facilitate future exchanges of ideas and insights between these disciplines.
Path Integral Monte Carlo Simulations of Warm Dense Plasmas with mid-Z Elements
NASA Astrophysics Data System (ADS)
Driver, Kevin; Soubiran, Francois; Zhang, Shuai; Militzer, Burkhard
2016-10-01
Theoretical studies of warm dense plasmas are crucial for improving our knowledge of giant planets, astrophysics, shock physics, and new plasma energy technologies, such as inertial confined fusion. Path integral Monte Carlo (PIMC) and density functional theory molecular dynamics (DFT-MD) provide consistent, first-principles descriptions of warm, dense matter over a wide range of density and temperature conditions. Here, we report simulation results for a variety of first- and second-row elements. DFT-MD algorithms are well-suited for low temperatures, while PIMC has been restricted to relatively high temperatures due to the free-particle approximation of the nodal surface. For heavier, second-row elements, we have developed a new, localized nodal surface, which allows us to treat bound states within the PIMC formalism. By combining PIMC and DFT-MD pressures and internal energies, we produce a coherent, first-principles equation of state, bridging the entire warm dense matter regime. Pair-correlation functions and the density of electronic states reveal an evolving plasma structure. The degree of ionization is affected by both temperature and density. Finally, shock Hugoniot curves show an increase in compression as the first and second shells are ionized. Funding provided by the DOE (DE-SC0010517). Computational resources provided by the NCAR/CISL, NERSC, and NASA.
The quantum nature of the hydrogen bond: insight from path-integral molecular dynamics
NASA Astrophysics Data System (ADS)
Walker, Brent; Li, Xin-Zheng; Michaelides, Angelos
2011-03-01
Hydrogen (H) bonds are weak, generally intermolecular bonds, that hold together much of soft matter, the condensed phases of water, network liquids, and many ferroelectric crystals. The small mass of H means H-bonds are inherently quantum mechanical; effects such as zero point motion and tunneling should be considered, although often are not. In particular, a consistent picture of quantum nuclear effects on the strength of H-bonds and consequently the structure of H-bonded systems is still absent. Here, we report ab initio path-integral molecular dynamics studies on the quantum nature of the H-bond. Systematic examination of a range of H-bonded systems shows that quantum nuclei weaken weak H-bonds but strengthen relatively strong ones. This correlation arises from a competition between anharmonic intermolecular bond bending and intramolecular bond stretching. A simple rule of thumb enables predictions to be made for H-bonded bonded materials in general with merely classical knowledge (e.g. H-bond strength or H-bond length). Our work rationalizes the contrasting influence of quantum nuclear dynamics on a wide variety of materials, including liquid water and HF, and highlights the need for flexible molecules in force-field based studies of quantum nuclear dynamics.
NASA Astrophysics Data System (ADS)
Mühlbacher, Lothar; Ankerhold, Joachim
2005-05-01
Electron transfer (ET) across molecular chains including an impurity is studied based on a recently improved real-time path-integral Monte Carlo (PIMC) approach [L. Mühlbacher, J. Ankerhold, and C. Escher, J. Chem. Phys. 121 12696 (2004)]. The reduced electronic dynamics is studied for various bridge lengths and defect site energies. By determining intersite hopping rates from PIMC simulations up to moderate times, the relaxation process in the extreme long-time limit is captured within a sequential transfer model. The total transfer rate is extracted and shown to be enhanced for certain defect site energies. Superexchange turns out to be relevant for extreme gap energies only and then gives rise to different dynamical signatures for high- and low-lying defects. Further, it is revealed that the entire bridge compound approaches a steady state on a much shorter time scale than that related to the total transfer. This allows for a simplified description of ET along donor-bridge-acceptor systems in the long-time range.
Path integral Monte Carlo and density functional molecular dynamics simulations of hot, dense helium
NASA Astrophysics Data System (ADS)
Militzer, B.
2009-04-01
Two first-principles simulation techniques, path integral Monte Carlo (PIMC) and density functional molecular dynamics (DFT-MD), are applied to study hot, dense helium in the density-temperature range of 0.387-5.35gcm-3 and 500K-1.28×108K . One coherent equation of state is derived by combining DFT-MD data at lower temperatures with PIMC results at higher temperatures. Good agreement between both techniques is found in an intermediate-temperature range. For the highest temperatures, the PIMC results converge to the Debye-Hückel limiting law. In order to derive the entropy, a thermodynamically consistent free-energy fit is used that reproduces the internal energies and pressure derived from the first-principles simulations. The equation of state is presented in the form of a table as well as a fit and is compared with different free-energy models. Pair-correlation functions and the electronic density of states are discussed. Shock Hugoniot curves are compared with recent laser shock-wave experiments.
Path-integral molecular dynamics simulation of 3C-SiC
NASA Astrophysics Data System (ADS)
Ramírez, Rafael; Herrero, Carlos P.; Hernández, Eduardo R.; Cardona, Manuel
2008-01-01
Molecular dynamics simulations of 3C-SiC have been performed as a function of pressure and temperature. These simulations treat both electrons and atomic nuclei by quantum mechanical methods. While the electronic structure of the solid is described by an efficient tight-binding Hamiltonian, the nuclei dynamics is treated by the path-integral formulation of statistical mechanics. To assess the relevance of nuclear quantum effects, the results of quantum simulations are compared to others where either the Si nuclei, the C nuclei, or both atomic nuclei are treated as classical particles. We find that the experimental thermal expansion of 3C-SiC is realistically reproduced by our simulations. The calculated bulk modulus of 3C-SiC and its pressure derivative at room temperature show also good agreement with the available experimental data. The effect of the electron-phonon interaction on the direct electronic gap of 3C-SiC has been calculated as a function of temperature and related to results obtained for bulk diamond and Si. Comparison to available experimental data shows satisfactory agreement, although we observe that the employed tight-binding model tends to overestimate the magnitude of the electron-phonon interaction. The effect of treating the atomic nuclei as classical particles on the direct gap of 3C-SiC has been assessed. We find that nonlinear quantum effects related to the atomic masses are particularly relevant at temperatures below 250K .
Path integration and cognitive mapping in a continuous attractor neural network model.
Samsonovich, A; McNaughton, B L
1997-08-01
A minimal synaptic architecture is proposed for how the brain might perform path integration by computing the next internal representation of self-location from the current representation and from the perceived velocity of motion. In the model, a place-cell assembly called a "chart" contains a two-dimensional attractor set called an "attractor map" that can be used to represent coordinates in any arbitrary environment, once associative binding has occurred between chart locations and sensory inputs. In hippocampus, there are different spatial relations among place fields in different environments and behavioral contexts. Thus, the same units may participate in many charts, and it is shown that the number of uncorrelated charts that can be encoded in the same recurrent network is potentially quite large. According to this theory, the firing of a given place cell is primarily a cooperative effect of the activity of its neighbors on the currently active chart. Therefore, it is not particularly useful to think of place cells as encoding any particular external object or event. Because of its recurrent connections, hippocampal field CA3 is proposed as a possible location for this "multichart" architecture; however, other implementations in anatomy would not invalidate the main concepts. The model is implemented numerically both as a network of integrate-and-fire units and as a "macroscopic" (with respect to the space of states) description of the system, based on a continuous approximation defined by a system of stochastic differential equations. It provides an explanation for a number of hitherto perplexing observations on hippocampal place fields, including doubling, vanishing, reshaping in distorted environments, acquiring directionality in a two-goal shuttling task, rapid formation in a novel environment, and slow rotation after disorientation. The model makes several new predictions about the expected properties of hippocampal place cells and other cells of the
Equilibrium fractionation of H and O isotopes in water from path integral molecular dynamics
NASA Astrophysics Data System (ADS)
Pinilla, Carlos; Blanchard, Marc; Balan, Etienne; Ferlat, Guillaume; Vuilleumier, Rodolphe; Mauri, Francesco
2014-06-01
The equilibrium fractionation factor between two phases is of importance for the understanding of many planetary and environmental processes. Although thermodynamic equilibrium can be achieved between minerals at high temperature, many natural processes involve reactions between liquids or aqueous solutions and solids. For crystals, the fractionation factor α can be theoretically determined using a statistical thermodynamic approach based on the vibrational properties of the phases. These calculations are mostly performed in the harmonic approximation, using empirical or ab-initio force fields. In the case of aperiodic and dynamic systems such as liquids or solutions, similar calculations can be done using finite-size molecular clusters or snapshots obtained from molecular dynamics (MD) runs. It is however difficult to assess the effect of these approximate models on the isotopic fractionation properties. In this work we present a systematic study of the calculation of the D/H and 18O/16O equilibrium fractionation factors in water for the liquid/vapour and ice/vapour phases using several levels of theory within the simulations. Namely, we use a thermodynamic integration approach based on Path Integral MD calculations (PIMD) and an empirical potential model of water. Compared with standard MD, PIMD takes into account quantum effects in the thermodynamic modeling of systems and the exact fractionation factor for a given potential can be obtained. We compare these exact results with those of modeling strategies usually used, which involve the mapping of the quantum system on its harmonic counterpart. The results show the importance of including configurational disorder for the estimation of isotope fractionation in liquid phases. In addition, the convergence of the fractionation factor as a function of parameters such as the size of the simulated system and multiple isotope substitution is analyzed, showing that isotope fractionation is essentially a local effect in
Ronacher, B; Westwig, E; Wehner, R
2006-09-01
When performing foraging trips desert ants of the genus Cataglyphis continuously process and update a ;home vector' that enables them to return to their nest on the shortest route. This capacity of path integration requires two types of information: (i) information about the travelling directions, and (ii) odometric information about the distances travelled in a particular direction. We have investigated how these two necessary pieces of information interact within the path integration processor. The specific question is: how do the ants process distance information if there is no simultaneous input from the sky compass available. Ants were trained to forage in a ;Z'-shaped channel system, the three segments of which joined at right angles. Individual animals were transferred from the feeder to a test field where their homing paths could be observed. In the crucial tests the middle segment of the maze was covered by orange Perspex that did not transmit the UV part of the spectrum, and thus precluded the perception of polarization patterns. Changes of the ant's processing of odometric information within this channel segment directly translate into a change in homing direction on the test field. The results indicate that the odometric information about travelling distance is largely ignored for path integration if there is no simultaneous input from the sky-view-based compass. They further show that idiothetic information cannot adequately substitute for the polarization compass to infer travelling directions.
Colosi, John A
2013-10-01
Previously published results from path integral theory for the horizontal coherence length utilized an empirical relation for the phase structure function density that was quite different from path integral results obtained for depth and time coherence where the phase structure function density was expanded to second order in the lag. This letter presents a result for horizontal coherence length which carries out the quadratic expansion and analytically solves the integral equations. Some simple calculations of horizontal coherence length demonstrate the differences between the present and old expressions. In contrast to the empirical result the present expression shows the expected one over square-root range and one over frequency scalings. The results also show more clearly how transverse coherence is sensitive to the space-time scales of internal waves and other environmental parameters.
Jang, Seogjoo; Voth, Gregory A
2017-05-07
Despite the fact that quantum mechanical principles do not allow the establishment of an exact quantum analogue of the classical transition state theory (TST), the development of a quantum TST (QTST) with a proper dynamical justification, while recovering the TST in the classical limit, has been a long standing theoretical challenge in chemical physics. One of the most recent efforts of this kind was put forth by Hele and Althorpe (HA) [J. Chem. Phys. 138, 084108 (2013)], which can be specified for any cyclically invariant dividing surface defined in the space of the imaginary time path integral. The present work revisits the issue of the non-uniqueness of QTST and provides a detailed theoretical analysis of HA-QTST for a general class of such path integral dividing surfaces. While we confirm that HA-QTST reproduces the result based on the ring polymer molecular dynamics (RPMD) rate theory for dividing surfaces containing only a quadratic form of low frequency Fourier modes, we find that it produces different results for those containing higher frequency imaginary time paths which accommodate greater quantum fluctuations. This result confirms the assessment made in our previous work [Jang and Voth, J. Chem. Phys. 144, 084110 (2016)] that HA-QTST does not provide a derivation of RPMD-TST in general and points to a new ambiguity of HA-QTST with respect to its justification for general cyclically invariant dividing surfaces defined in the space of imaginary time path integrals. Our analysis also offers new insights into similar path integral based QTST approaches.
Barnett-Cowan, Michael; Meilinger, Tobias; Vidal, Manuel; Teufel, Harald; Bülthoff, Heinrich H
2012-05-10
Path integration is a process in which self-motion is integrated over time to obtain an estimate of one's current position relative to a starting point (1). Humans can do path integration based exclusively on visual (2-3), auditory (4), or inertial cues (5). However, with multiple cues present, inertial cues - particularly kinaesthetic - seem to dominate (6-7). In the absence of vision, humans tend to overestimate short distances (<5 m) and turning angles (<30°), but underestimate longer ones (5). Movement through physical space therefore does not seem to be accurately represented by the brain. Extensive work has been done on evaluating path integration in the horizontal plane, but little is known about vertical movement (see (3) for virtual movement from vision alone). One reason for this is that traditional motion simulators have a small range of motion restricted mainly to the horizontal plane. Here we take advantage of a motion simulator (8-9) with a large range of motion to assess whether path integration is similar between horizontal and vertical planes. The relative contributions of inertial and visual cues for path navigation were also assessed. 16 observers sat upright in a seat mounted to the flange of a modified KUKA anthropomorphic robot arm. Sensory information was manipulated by providing visual (optic flow, limited lifetime star field), vestibular-kinaesthetic (passive self motion with eyes closed), or visual and vestibular-kinaesthetic motion cues. Movement trajectories in the horizontal, sagittal and frontal planes consisted of two segment lengths (1st: 0.4 m, 2nd: 1 m; ±0.24 m/s(2) peak acceleration). The angle of the two segments was either 45° or 90°. Observers pointed back to their origin by moving an arrow that was superimposed on an avatar presented on the screen. Observers were more likely to underestimate angle size for movement in the horizontal plane compared to the vertical planes. In the frontal plane observers were more likely to
NASA Technical Reports Server (NTRS)
Singh, Upendra N.; Refaat, Tamer F.; Petros, Mulugeta
2017-01-01
The societal benefits of understanding climate change through identification of global carbon dioxide sources and sinks led to the desired NASA's active sensing of carbon dioxide emissions over nights, days, and seasons (ASCENDS) space-based missions of global carbon dioxide measurements. For more than 15 years, NASA Langley Research Center (LaRC) have developed several carbon dioxide active remote sensors using the differential absorption lidar (DIAL) technique operating at the two-micron wavelength. Currently, an airborne two-micron triple-pulse integrated path differential absorption (IPDA) lidar is under development. This IPDA lidar measures carbon dioxide as well as water vapor, the dominant interfering molecule on carbon dioxide remote sensing. Advancement of this triple-pulse IPDA lidar development is presented.
Mouhat, Félix; Sorella, Sandro; Vuilleumier, Rodolphe; Saitta, Antonino Marco; Casula, Michele
2017-06-13
We introduce a novel approach for a fully quantum description of coupled electron-ion systems from first principles. It combines the variational quantum Monte Carlo solution of the electronic part with the path integral formalism for the quantum nuclear dynamics. On the one hand, the path integral molecular dynamics includes nuclear quantum effects by adding a set of fictitious classical particles (beads) aimed at reproducing nuclear quantum fluctuations via a harmonic kinetic term. On the other hand, variational quantum Monte Carlo can provide Born-Oppenheimer potential energy surfaces with a precision comparable to the most-advanced post-Hartree-Fock approaches, and with a favorable scaling with the system size. In order to cope with the intrinsic noise due to the stochastic nature of quantum Monte Carlo methods, we generalize the path integral molecular dynamics using a Langevin thermostat correlated according to the covariance matrix of quantum Monte Carlo nuclear forces. The variational parameters of the quantum Monte Carlo wave function are evolved during the nuclear dynamics, such that the Born-Oppenheimer potential energy surface is unbiased. Statistical errors on the wave function parameters are reduced by resorting to bead grouping average, which we show to be accurate and well-controlled. Our general algorithm relies on a Trotter breakup between the dynamics driven by ionic forces and the one set by the harmonic interbead couplings. The latter is exactly integrated, even in the presence of the Langevin thermostat, thanks to the mapping onto an Ornstein-Uhlenbeck process. This framework turns out to be also very efficient in the case of noiseless (deterministic) ionic forces. The new implementation is validated on the Zundel ion (H5O2(+)) by direct comparison with standard path integral Langevin dynamics calculations made with a coupled cluster potential energy surface. Nuclear quantum effects are confirmed to be dominant over thermal effects well beyond
Makri, Nancy
2014-10-07
The real-time path integral representation of the reduced density matrix for a discrete system in contact with a dissipative medium is rewritten in terms of the number of blips, i.e., elementary time intervals over which the forward and backward paths are not identical. For a given set of blips, it is shown that the path sum with respect to the coordinates of all remaining time points is isomorphic to that for the wavefunction of a system subject to an external driving term and thus can be summed by an inexpensive iterative procedure. This exact decomposition reduces the number of terms by a factor that increases exponentially with propagation time. Further, under conditions (moderately high temperature and/or dissipation strength) that lead primarily to incoherent dynamics, the “fully incoherent limit” zero-blip term of the series provides a reasonable approximation to the dynamics, and the blip series converges rapidly to the exact result. Retention of only the blips required for satisfactory convergence leads to speedup of full-memory path integral calculations by many orders of magnitude.
Response statistics of rotating shaft with non-linear elastic restoring forces by path integration
NASA Astrophysics Data System (ADS)
Gaidai, Oleg; Naess, Arvid; Dimentberg, Michael
2017-07-01
Extreme statistics of random vibrations is studied for a Jeffcott rotor under uniaxial white noise excitation. Restoring force is modelled as elastic non-linear; comparison is done with linearized restoring force to see the force non-linearity effect on the response statistics. While for the linear model analytical solutions and stability conditions are available, it is not generally the case for non-linear system except for some special cases. The statistics of non-linear case is studied by applying path integration (PI) method, which is based on the Markov property of the coupled dynamic system. The Jeffcott rotor response statistics can be obtained by solving the Fokker-Planck (FP) equation of the 4D dynamic system. An efficient implementation of PI algorithm is applied, namely fast Fourier transform (FFT) is used to simulate dynamic system additive noise. The latter allows significantly reduce computational time, compared to the classical PI. Excitation is modelled as Gaussian white noise, however any kind distributed white noise can be implemented with the same PI technique. Also multidirectional Markov noise can be modelled with PI in the same way as unidirectional. PI is accelerated by using Monte Carlo (MC) estimated joint probability density function (PDF) as initial input. Symmetry of dynamic system was utilized to afford higher mesh resolution. Both internal (rotating) and external damping are included in mechanical model of the rotor. The main advantage of using PI rather than MC is that PI offers high accuracy in the probability distribution tail. The latter is of critical importance for e.g. extreme value statistics, system reliability, and first passage probability.
Hayes, Robin L; Paddison, Stephen J; Tuckerman, Mark E
2009-12-31
The mono-, di-, and tetrahydrates of trifluoromethanesulfonic acid, which contain characteristic H(3)O(+), H(5)O(2)(+), and H(9)O(4)(+) structures, provide model systems for understanding proton transport in materials with high perfluorosulfonic acid density such as perfluorosulfonic acid membranes commonly employed in hydrogen fuel cells. Ab initio molecular dynamics simulations indicate that protons in these solids are predisposed to transfer to the water most strongly bound to sulfonate groups via a Grotthuss-type mechanism, but quickly return to the most solvated defect structure either due to the lack of a nearby species to stabilize the new defect or a preference for the proton to be maximally hydrated. Path integral molecular dynamics of the mono- and dihydrate reveal significant quantum effects that facilitate proton transfer to the "presolvated" water or SO(3)(-) in the first solvation shell and increase the Zundel character of all the defects. These trends are quantified in free energy profiles for each bonding environment. Hydrogen bonding criteria for HOH-OH(2) and HOH-O(3)S are extracted from the two-dimensional potential of mean force. The quantum radial distribution function, radius of gyration, and root-mean-square displacement position correlation function show that the protonic charge is distributed over two or more water molecules. Metastable structural defects with one excess proton shared between two sulfonate groups and another Zundel or Eigen type cation defect are found for the mono- and dihydrate but not for the tetrahydrate crystal. Results for the tetrahydrate native crystal exhibit minor differences at 210 and 250 K. IR spectra are calculated for all native and stable defect structures. Graph theory techniques are used to characterize the chain lengths and ring sizes in the hydrogen bond network. Low conductivities when limited water is present may be attributable to trapping of protons between SO(3)(-) groups and the increased
Different strategies for spatial updating in yaw and pitch path integration
Goeke, Caspar M.; König, Peter; Gramann, Klaus
2013-01-01
Research in spatial navigation revealed the existence of discrete strategies defined by the use of distinct reference frames during virtual path integration. The present study investigated the distribution of these navigation strategies as a function of gender, video gaming experience, and self-estimates of spatial navigation abilities in a population of 300 subjects. Participants watched videos of virtual passages through a star-field with one turn in either the horizontal (yaw) or the vertical (pitch) axis. At the end of a passage they selected one out of four homing arrows to indicate the initial starting location. To solve the task, participants could employ two discrete strategies, navigating within either an egocentric or an allocentric reference frame. The majority of valid subjects (232/260) consistently used the same strategy in more than 75% of all trials. With that approach 33.1% of all participants were classified as Turners (using an egocentric reference frame on both axes) and 46.5% as Non-turners (using an allocentric reference frame on both axes). 9.2% of all participants consistently used an egocentric reference frame in the yaw plane but an allocentric reference frame in the pitch plane (Switcher). Investigating the influence of gender on navigation strategies revealed that females predominantly used the Non-turner strategy while males used both the Turner and the Non-turner strategy with comparable probabilities. Other than expected, video gaming experience did not influence strategy use. Based on a strong quantitative basis with the sample size about an order of magnitude larger than in typical psychophysical studies these results demonstrate that most people reliably use one out of three possible navigation strategies (Turners, Non-turners, Switchers) for spatial updating and provides a sound estimate of how those strategies are distributed within the general population. PMID:23412683
NASA Astrophysics Data System (ADS)
Sun, X.; Abshire, J. B.; Ramanathan, A. K.; Mao, J.; Kawa, S. R.
2016-12-01
A multi-wavelength sampling integrated path differential (IPDA) CO2 lidar is analyzed and modeled. The instrument transmits laser pulses at a series of wavelengths across the 1572.33 nm CO2 absorption line. The receiver measures the received laser pulse energy and time of flight at each wavelength. The measurements are then fit to a CO2 absorption line shape to determine the total column CO2 mixing ratio. The receiver model includes effects of solar background, photon detection shot noise, detector dark current, preamplifier noise and laser speckle noise. The least-square curve fit is a linear fit in the optical depth domain and the logarithm of the raw measurements. The column CO2 mixing ratio is proportional to the scaling factor resulted from the curve fit. There are several advantages to performing the curve fit in the optical depth domain: (a) the result is directly proportional to the CO2molecule number density of the column; (b) it is a standard linear least square error fit where the theory is well established; (c) there is no need to separately estimate the off-line optical transmission. The receiver model further gives insight about the effects of various instrument parameters and the difference between the atmosphere model used in the curve fit and the actual atmosphere. For example, we can use the model to estimate the biases in the retrieved CO2 mixing ratio from small errors in the meteorological data used to generate the line shape used in the curve fit. We have shown that the estimated instrument performance using this receiver model agrees with the results from our recent airborne measurements. The receiver model is also used in the simulation of the impact of the lidar measurements of the global greenhouse gas distribution and their projected impact on quantification of surface sources and sinks.
NASA Astrophysics Data System (ADS)
Koda, Shin-Ichi; Takatsuka, Kazuo
2011-03-01
The coherent path integral is generalized such that the identity operator represented in a complete (actually overcomplete) set of the coherent states with the “time-variable” exponents are inserted between two consecutive short-time propagators. Since such a complete set of any given exponent can constitute the identity operator, the exponent may be varied from time to time without loss of generality as long as it is set common to all the Gaussians. However, a finite truncation of the coherent state expansion should result in different values of the propagator depending on the choice of the exponents. Furthermore, approximation methodology to treat with the exact propagator can also depend on this choice, and thereby many different semiclassical propagators may emerge from these combinations. Indeed, we show that the well-known semiclassical propagators such as those of Van Vleck, Herman-Kluk, Heller’s thawed Gaussian, and many others can be derived in a systematic manner, which enables one to comprehend these semiclassical propagators from a unified point of view. We are particularly interested in our generalized form of the Herman-Kluk propagator, since the relative accuracy of this propagator has been well established by Kay, and since, nevertheless, its derivation was not necessarily clear. Thus our generalized Herman-Kluk propagator replaces the classical Hamiltonian with a Gaussian averaged quantum Hamiltonian, generating non-Newtonian trajectories. We perform a numerical test to assess the quality of such a family of generalized Herman-Kluk propagators and find that the original Herman-Kluk gives an accurate result. The reason why this has come about is also discussed.
Different strategies for spatial updating in yaw and pitch path integration.
Goeke, Caspar M; König, Peter; Gramann, Klaus
2013-01-01
Research in spatial navigation revealed the existence of discrete strategies defined by the use of distinct reference frames during virtual path integration. The present study investigated the distribution of these navigation strategies as a function of gender, video gaming experience, and self-estimates of spatial navigation abilities in a population of 300 subjects. Participants watched videos of virtual passages through a star-field with one turn in either the horizontal (yaw) or the vertical (pitch) axis. At the end of a passage they selected one out of four homing arrows to indicate the initial starting location. To solve the task, participants could employ two discrete strategies, navigating within either an egocentric or an allocentric reference frame. The majority of valid subjects (232/260) consistently used the same strategy in more than 75% of all trials. With that approach 33.1% of all participants were classified as Turners (using an egocentric reference frame on both axes) and 46.5% as Non-turners (using an allocentric reference frame on both axes). 9.2% of all participants consistently used an egocentric reference frame in the yaw plane but an allocentric reference frame in the pitch plane (Switcher). Investigating the influence of gender on navigation strategies revealed that females predominantly used the Non-turner strategy while males used both the Turner and the Non-turner strategy with comparable probabilities. Other than expected, video gaming experience did not influence strategy use. Based on a strong quantitative basis with the sample size about an order of magnitude larger than in typical psychophysical studies these results demonstrate that most people reliably use one out of three possible navigation strategies (Turners, Non-turners, Switchers) for spatial updating and provides a sound estimate of how those strategies are distributed within the general population.
NASA Astrophysics Data System (ADS)
Ishii, S.; Koyama, M.; Baron, P.; Iwai, H.; Mizutani, K.; Itabe, T.; Sato, A.; Asai, K.
2013-05-01
The National Institute of Information and Communications Technology (NICT) has made a great deal of effort to develop a coherent 2 μm differential absorption and wind lidar (Co2DiaWiL) for measuring CO2 and wind speed. First, coherent Integrated Path Differential Absorption (IPDA) lidar experiments were conducted using the Co2DiaWiL and a foothill target (tree and ground surface) located about 7.12 km south of NICT on 11, 27, and 28 December 2010. The detection sensitivity of a 2 μm IPDA lidar was examined in detail using the CO2 concentration measured by the foothill reflection. The precisions of CO2 measurements for the foothill target and 900, 4500 and 27 000 shot pairs were 6.5, 2.8, and 1.2%, respectively. The results indicated that a coherent IPDA lidar with a laser operating at a high pulse repetition frequency of a few tens of KHz is necessary for XCO2 (column-averaged dry air mixing ratio of CO2) measurement with a precision of 1-2 ppm in order to observe temporal and spatial variations in the CO2. Statistical comparisons indicated that, although a small amount of in situ data and the fact that they were not co-located with the foothill target made comparison difficult, the CO2 volume mixing ratio obtained by the Co2DiaWiL measurements for the foothill target and atmospheric returns was about -5 ppm lower than the 5 min running averages of the in situ sensor. Not only actual difference of sensing volume or the natural variability of CO2 but also the fluctuations of temperature could cause this difference. The statistical results indicated that there were no biases between the foothill target and atmospheric return measurements. The 2 μm coherent IPDA lidar can detect the CO2 volume mixing ratio change of 3% in the 5 min signal integration. In order to detect the position of the foothill target, to measure a range with a high SNR (signal-to-noise ratio), and to reduce uncertainty due to the presence of aerosols and clouds, it is important to make a
Lagin, L J; Bettenhauasen, R C; Bowers, G A; Carey, R W; Edwards, O D; Estes, C M; Demaret, R D; Ferguson, S W; . Fisher, J M; Ho, J C; Ludwigsen, A P; Mathisen, D G; Marshall, C D; Matone, J M; McGuigan, D L; Sanchez, R J; Shelton, R T; Stout, E A; Tekle, E; Townsend, S L; Van Arsdall, P J; Wilson, E F
2007-09-11
diagnostics, in preparation for project completion in 2009. Additional capabilities to support fusion ignition shots in a National Ignition Campaign (NIC) beginning in 2010 will include a cryogenic target system, target diagnostics, and integrated experimental shot data analysis with tools for data visualization and archiving. This talk discusses the current status of the control system implementation and discusses the plan to complete the control system on the path to ignition.
Durlak, Piotr; Morrison, Carole A; Middlemiss, Derek S; Latajka, Zdzislaw
2007-08-14
We have studied the double proton transfer (DPT) reaction in the cyclic dimer of chloroacetic acid using both classical and path integral Car-Parrinello molecular dynamics. We also attempt to quantify the errors in the potential energy surface that arise from the use of a pure density functional. In the classical dynamics a clear reaction mechanism can be identified, where asynchronized DPT arises due to coupling between the O-H stretching oscillator and several low energy intermolecular vibrational modes. This mechanism is considerably altered when quantum tunneling is permitted in the simulation. The introduction of path integrals leads to considerable changes in the thermally averaged molecular geometry, leading to shorter and more centered hydrogen bond linkages.
Exact solution of the Feynman-Kac path integral for a point potential in an infinite square well
NASA Astrophysics Data System (ADS)
Rejcek, James M.; Fazleev, Nail G.; Fry, John L.
2004-10-01
The solution of the Feynman-Kac path integral for a point potential in an infinite square well can be understood in terms of symmetric and anti-symmetric eigenstates of the Hamiltonian. If one is not careful in the use of the boundary conditions, it would appear that the even reflection states are not allowed as the solutions. Numerical simulation results for the Feynman-Kac path integral are compared with the analytical solutions. It is also shown that as the magnitude of the point potential is increased the energy spectrum shifts to higher values, and the energy eigenvalues approach the solutions obtained for an infinite well half the size of the original. This effect has implications on the entropy problem known as Maxwell's Demon.
NASA Astrophysics Data System (ADS)
Khodja, A.; Kadja, A.; Benamira, F.; Guechi, L.
2017-07-01
The problem of a Klein-Gordon particle moving in equal vector and scalar Rosen-Morse-type potentials is solved in the framework of Feynman's path integral approach. Explicit path integration leads to a closed form for the radial Green's function associated with different shapes of the potentials. For q≤-1 , and 1/2α ln | q|
NASA Astrophysics Data System (ADS)
Durlak, Piotr; Morrison, Carole A.; Middlemiss, Derek S.; Latajka, Zdzislaw
2007-08-01
We have studied the double proton transfer (DPT) reaction in the cyclic dimer of chloroacetic acid using both classical and path integral Car-Parrinello molecular dynamics. We also attempt to quantify the errors in the potential energy surface that arise from the use of a pure density functional. In the classical dynamics a clear reaction mechanism can be identified, where asynchronized DPT arises due to coupling between the O-H stretching oscillator and several low energy intermolecular vibrational modes. This mechanism is considerably altered when quantum tunneling is permitted in the simulation. The introduction of path integrals leads to considerable changes in the thermally averaged molecular geometry, leading to shorter and more centered hydrogen bond linkages.
Benamira, F.; Guechi, L.; Mameri, S.; Sadoun, M. A.
2010-03-15
The Green's function for a Klein-Gordon particle under the action of vector plus scalar deformed Hulthen and Woods-Saxon potentials is evaluated by exact path integration. Explicit path integration leads to the Green's function for different shapes of the potentials. From the singularities of the latter Green's function, the bound states are extracted. For q{>=}1 and (1/{alpha})ln q
NASA Astrophysics Data System (ADS)
Cugliandolo, Leticia F.; Lecomte, Vivien
2017-08-01
The definition and manipulation of Langevin equations with multiplicative white noise require special care (one has to specify the time discretisation and a stochastic chain rule has to be used to perform changes of variables). While discretisation-scheme transformations and non-linear changes of variable can be safely performed on the Langevin equation, these same transformations lead to inconsistencies in its path-integral representation. We identify their origin and we show how to extend the well-known Ito prescription (dB2 = dt ) in a way that defines a modified stochastic calculus to be used inside the path-integral representation of the process, in its Onsager-Machlup form.
Ab initio path integral molecular dynamics simulation study on the dihydrogen bond of NH4+⋯BeH2
NASA Astrophysics Data System (ADS)
Hayashi, Aiko; Shiga, Motoyuki; Tachikawa, Masanori
2005-07-01
An ab initio path integral molecular dynamics simulation has been performed to study the quantum and thermal effects of a dihydrogen bonded cation, NH4+⋯BeH2. In this system, an attractive interaction exists between two neighboring hydrogen atoms as N δ- H δ+ ⋯H δ- Be δ+ involving large-amplitude of vibration. Some properties playing a key role for this dihydrogen bonded system, such as the bond length, bond angle, and distribution of atomic charges, are investigated in detail by comparing the results of path integral and classical molecular dynamics with those of the equilibrium structure. It was found that the atomic charges of H δ+ and H δ- are decreased and the dihydrogen H δ+ ⋯H δ- bond length is expanded as the thermal and zero-point quantum effects.
NASA Astrophysics Data System (ADS)
Kamibayashi, Yuki; Miura, Shinichi
2016-08-01
In the present study, variational path integral molecular dynamics and associated hybrid Monte Carlo (HMC) methods have been developed on the basis of a fourth order approximation of a density operator. To reveal various parameter dependence of physical quantities, we analytically solve one dimensional harmonic oscillators by the variational path integral; as a byproduct, we obtain the analytical expression of the discretized density matrix using the fourth order approximation for the oscillators. Then, we apply our methods to realistic systems like a water molecule and a para-hydrogen cluster. In the HMC, we adopt two level description to avoid the time consuming Hessian evaluation. For the systems examined in this paper, the HMC method is found to be about three times more efficient than the molecular dynamics method if appropriate HMC parameters are adopted; the advantage of the HMC method is suggested to be more evident for systems described by many body interaction.
NASA Astrophysics Data System (ADS)
Wagner, Gerd; Maxwell, Stephen; Plusquellic, David
2016-06-01
Integrated path concentrations of ambient levels of carbon dioxide and methane have been measured during nighttime periods at NIST, Boulder (CO, USA), using a ground-based, eyesafe laser system. In this contribution, we describe the transmitter and receiver system, demonstrate measurements of CO2 and CH4 in comparison with an in situ point sensor measurement using a commercial cavity ring-down instrument, and demonstrate a speckle noise reduction method.
NASA Astrophysics Data System (ADS)
Ingber, Lester; Nunez, Paul L.
1995-05-01
We present high-resolution path-integral calculations of a previously developed model of short-term memory in neocortex. These calculations, made possible with supercomputer resources, supplant similar calculations made by Ingber [Phys. Rev. E 49, 4652 (1994)] and support coarser estimates made by Ingber [Phys. Rev. A 29, 3346 (1984)]. We also present a current experimental context for the relevance of these calculations using the approach of statistical mechanics of neocortical interactions, especially in the context of electroencephalographic data.
NASA Astrophysics Data System (ADS)
Fix, Andreas; Quatrevalet, Mathieu; Witschas, Benjamin; Wirth, Martin; Büdenbender, Christian; Amediek, Axel; Ehret, Gerhard
2016-06-01
The stringent requirements for both the frequency stability and power reference represent a challenging task for Integrated Path Differential Absorption Lidars (IPDA) to measure greenhouse gas columns from satellite or aircraft. Currently, the German-French methane mission MERLIN (Methan Remote Lidar Mission) is prepared. At the same time CHARM-F, an aircraft installed system has been developed at DLR as an airborne demonstrator for a spaceborne greenhouse gas mission. The concepts and realization of these important sub-systems are discussed.
NASA Astrophysics Data System (ADS)
Bock, Wolfgang; Capraro, Patrick
2017-02-01
We identify the integrand for the Hamiltonian path integral in space representation as a Kondratiev distribution. For this purpose we use methods from white noise analysis to compute also the Green's function of the underlying Schrödinger equation. We show that its generalized expectation solves the Schrödinger equation and that a functional form of the canonical commutation realtions is fulfilled.
On Dirac-Coulomb problem in (2+1) dimensional space-time and path integral quantization
Haouat, S.; Chetouani, L.
2012-06-15
The problem of Dirac particle interacting with Coulomb potential in (2+1) dimensions is formulated in the framework of super-symmetric path integrals where the spin degrees of freedom are described by odd Grassmannian variables. The relative propagator is expressed through Cartesian coordinates in a Hamiltonian form by the use of an adequate transformation. The passage to the polar coordinates permitted us to calculate the fixed energy Green's function and to extract bound states and associating wave functions.
NASA Astrophysics Data System (ADS)
Predescu, Cristian
2004-05-01
In this paper I provide significant mathematical evidence in support of the existence of direct short-time approximations of any polynomial order for the computation of density matrices of physical systems described by arbitrarily smooth and bounded from below potentials. While for Theorem 2, which is “experimental,” I only provide a “physicist’s” proof, I believe the present development is mathematically sound. As a verification, I explicitly construct two short-time approximations to the density matrix having convergence orders 3 and 4, respectively. Furthermore, in Appendix B, I derive the convergence constant for the trapezoidal Trotter path integral technique. The convergence orders and constants are then verified by numerical simulations. While the two short-time approximations constructed are of sure interest to physicists and chemists involved in Monte Carlo path integral simulations, the present paper is also aimed at the mathematical community, who might find the results interesting and worth exploring. I conclude the paper by discussing the implications of the present findings with respect to the solvability of the dynamical sign problem appearing in real-time Feynman path integral simulations.
Hironaka, Mantaro; Tojo, Sumio; Nomakuchi, Shintaro; Filippi, Lisa; Hariyama, Takahiko
2007-06-01
Females of the subsocial shield bug, Parastrachia japonensis (Parastrachiidae), are central-place foragers, collecting drupes for their young from nearby host trees by walking along the forest floor both during the day and at night. Because burrows are often some distance from the drupe-shedding tree, the bugs must repeatedly leave their burrows, search for drupes, and return to the burrows. After a bug leaves its burrow, it searches arduously until it encounters a drupe. When a drupe is obtained, the bug always takes the shortest route back to its burrow. It has been clarified that this bug utilizes path integration during diurnal provisioning excursions. In this paper, we examined nocturnal behavior and some parameters of the path integration utilized by P. japonensis. There were no observable differences between day and night in the patterns of foraging and direct-homing behavior. When the bug was displaced to another position during the day or night, it always walked straight toward the fictive burrow, the site where the burrow should be if it had been displaced along with the bug, and then displayed searching behavior in the vicinity of the fictive burrow. The distance of the straight run corresponded accurately with a straight line between the burrow and the place where the bug obtained the drupe. These results indicate that P. japonensis orients toward the burrow using path integration both during diurnal and nocturnal provisioning behavior.
NASA Astrophysics Data System (ADS)
Agarwal, Animesh; Delle Site, Luigi
2015-09-01
Quantum effects due to the spatial delocalization of light atoms are treated in molecular simulation via the path integral technique. Among several methods, Path Integral (PI) Molecular Dynamics (MD) is nowadays a powerful tool to investigate properties induced by spatial delocalization of atoms; however, computationally this technique is very demanding. The above mentioned limitation implies the restriction of PIMD applications to relatively small systems and short time scales. One of the possible solutions to overcome size and time limitation is to introduce PIMD algorithms into the Adaptive Resolution Simulation Scheme (AdResS). AdResS requires a relatively small region treated at path integral level and embeds it into a large molecular reservoir consisting of generic spherical coarse grained molecules. It was previously shown that the realization of the idea above, at a simple level, produced reasonable results for toy systems or simple/test systems like liquid parahydrogen. Encouraged by previous results, in this paper, we show the simulation of liquid water at room conditions where AdResS, in its latest and more accurate Grand-Canonical-like version (GC-AdResS), is merged with two of the most relevant PIMD techniques available in the literature. The comparison of our results with those reported in the literature and/or with those obtained from full PIMD simulations shows a highly satisfactory agreement.
Agarwal, Animesh Delle Site, Luigi
2015-09-07
Quantum effects due to the spatial delocalization of light atoms are treated in molecular simulation via the path integral technique. Among several methods, Path Integral (PI) Molecular Dynamics (MD) is nowadays a powerful tool to investigate properties induced by spatial delocalization of atoms; however, computationally this technique is very demanding. The above mentioned limitation implies the restriction of PIMD applications to relatively small systems and short time scales. One of the possible solutions to overcome size and time limitation is to introduce PIMD algorithms into the Adaptive Resolution Simulation Scheme (AdResS). AdResS requires a relatively small region treated at path integral level and embeds it into a large molecular reservoir consisting of generic spherical coarse grained molecules. It was previously shown that the realization of the idea above, at a simple level, produced reasonable results for toy systems or simple/test systems like liquid parahydrogen. Encouraged by previous results, in this paper, we show the simulation of liquid water at room conditions where AdResS, in its latest and more accurate Grand-Canonical-like version (GC-AdResS), is merged with two of the most relevant PIMD techniques available in the literature. The comparison of our results with those reported in the literature and/or with those obtained from full PIMD simulations shows a highly satisfactory agreement.
Schmidt, Matthew; Constable, Steve; Ing, Christopher; Roy, Pierre-Nicholas
2014-06-21
We developed and studied the implementation of trial wavefunctions in the newly proposed Langevin equation Path Integral Ground State (LePIGS) method [S. Constable, M. Schmidt, C. Ing, T. Zeng, and P.-N. Roy, J. Phys. Chem. A 117, 7461 (2013)]. The LePIGS method is based on the Path Integral Ground State (PIGS) formalism combined with Path Integral Molecular Dynamics sampling using a Langevin equation based sampling of the canonical distribution. This LePIGS method originally incorporated a trivial trial wavefunction, ψ{sub T}, equal to unity. The present paper assesses the effectiveness of three different trial wavefunctions on three isotopes of hydrogen for cluster sizes N = 4, 8, and 13. The trial wavefunctions of interest are the unity trial wavefunction used in the original LePIGS work, a Jastrow trial wavefunction that includes correlations due to hard-core repulsions, and a normal mode trial wavefunction that includes information on the equilibrium geometry. Based on this analysis, we opt for the Jastrow wavefunction to calculate energetic and structural properties for parahydrogen, orthodeuterium, and paratritium clusters of size N = 4 − 19, 33. Energetic and structural properties are obtained and compared to earlier work based on Monte Carlo PIGS simulations to study the accuracy of the proposed approach. The new results for paratritium clusters will serve as benchmark for future studies. This paper provides a detailed, yet general method for optimizing the necessary parameters required for the study of the ground state of a large variety of systems.
Arnold, Corey W; Wallace, W Dean; Chen, Shawn; Oh, Andrea; Abtin, Fereidoun; Genshaft, Scott; Binder, Scott; Aberle, Denise; Enzmann, Dieter
2016-01-01
The current paradigm of cancer diagnosis involves uncoordinated communication of findings from radiology and pathology to downstream physicians. Discordance between these findings can require additional time from downstream users to resolve, or given incorrect resolution, may adversely impact treatment decisions. To mitigate this problem, we developed a web-based system, called RadPath, for correlating and integrating radiology and pathology reporting. RadPath includes interfaces to our institution's clinical information systems, which are used to retrieve reports, images, and test results that are structured into an interactive compendium for a diagnostic patient case. The system includes an editing interface for physicians, allowing for the inclusion of additional clinical data, as well as the ability to retrospectively correlate and contextualize imaging findings following pathology diagnosis. During pilot deployment and testing over the course of 1 year, physicians at our institution have completed 60 RadPath cases, requiring an average of 128 seconds from a radiologist and an average of 93 seconds from a pathologist per case. Several technical and workflow challenges were encountered during development, including interfacing with diverse clinical information systems, automatically structuring report contents, and determining the appropriate physicians to create RadPath summaries. Reaction to RadPath has been positive, with users valuing the system's ability to consolidate diagnostic information. With the increasing complexity of medicine and the movement toward team-based disease management, there is a need for improved clinical communication and information exchange. RadPath provides a platform for generating coherent and correlated diagnostic summaries in cancer diagnosis with minimal additional effort from physicians. Copyright © 2016 The Association of University Radiologists. Published by Elsevier Inc. All rights reserved.
Hayes, Robin L; Paddison, Stephen J; Tuckerman, Mark E
2011-06-16
Trifluoromethanesulfonic acid hydrates provide a well-defined system to study proton dissociation and transport in perfluorosulfonic acid membranes, typically used as the electrolyte in hydrogen fuel cells, in the limit of minimal water. The triflic acid pentahydrate crystal (CF(3)SO(3)H·5H(2)O) is sufficiently aqueous that it contains an extended three-dimensional water network. Despite it being extended, however, long-range proton transport along the network is structurally unfavorable and would require considerable rearrangement. Nevertheless, the triflic acid pentahydrate crystal system can provide a clear picture of the preferred locations of local protonic defects in the water network, which provides insights about related structures in the disordered, low-hydration environment of perfluorosulfonic acid membranes. Ab initio molecular dynamics simulations reveal that the proton defect is most likely to transfer to the closest water that has the expected presolvation and only contains water in its first solvation shell. Unlike the tetrahydrate of triflic acid (CF(3)SO(3)H·4H(2)O), there is no evidence of the proton preferentially transferring to a water molecule bridging two of the sulfonate groups. However, this could be an artifact of the crystal structure since the only such water molecule is separated from the proton by long O-O distances. Hydrogen bonding criteria, using the two-dimensional potential of mean force, are extracted. Radial distribution functions, free energy profiles, radii of gyration, and the root-mean-square displacement computed from ab initio path integral molecular dynamics simulations reveal that quantum effects do significantly extend the size of the protonic defect and increase the frequency of proton transfer events by nearly 15%. The calculated IR spectra confirm that the dominant protonic defect mostly exists as an Eigen cation but contains some Zundel ion characteristics. Chain lengths and ring sizes determined from the
NASA Astrophysics Data System (ADS)
Montoya-Castillo, Andrés; Reichman, David R.
2017-01-01
We derive a semi-analytical form for the Wigner transform for the canonical density operator of a discrete system coupled to a harmonic bath based on the path integral expansion of the Boltzmann factor. The introduction of this simple and controllable approach allows for the exact rendering of the canonical distribution and permits systematic convergence of static properties with respect to the number of path integral steps. In addition, the expressions derived here provide an exact and facile interface with quasi- and semi-classical dynamical methods, which enables the direct calculation of equilibrium time correlation functions within a wide array of approaches. We demonstrate that the present method represents a practical path for the calculation of thermodynamic data for the spin-boson and related systems. We illustrate the power of the present approach by detailing the improvement of the quality of Ehrenfest theory for the correlation function Cz z(t ) =Re ⟨σz(0 ) σz(t ) ⟩ for the spin-boson model with systematic convergence to the exact sampling function. Importantly, the numerically exact nature of the scheme presented here and its compatibility with semiclassical methods allows for the systematic testing of commonly used approximations for the Wigner-transformed canonical density.
Montoya-Castillo, Andrés; Reichman, David R
2017-01-14
We derive a semi-analytical form for the Wigner transform for the canonical density operator of a discrete system coupled to a harmonic bath based on the path integral expansion of the Boltzmann factor. The introduction of this simple and controllable approach allows for the exact rendering of the canonical distribution and permits systematic convergence of static properties with respect to the number of path integral steps. In addition, the expressions derived here provide an exact and facile interface with quasi- and semi-classical dynamical methods, which enables the direct calculation of equilibrium time correlation functions within a wide array of approaches. We demonstrate that the present method represents a practical path for the calculation of thermodynamic data for the spin-boson and related systems. We illustrate the power of the present approach by detailing the improvement of the quality of Ehrenfest theory for the correlation function Czz(t)=Re⟨σz(0)σz(t)⟩ for the spin-boson model with systematic convergence to the exact sampling function. Importantly, the numerically exact nature of the scheme presented here and its compatibility with semiclassical methods allows for the systematic testing of commonly used approximations for the Wigner-transformed canonical density.
Shek, Daniel T. L.
2012-01-01
An integration of the qualitative evaluation findings collected from program implementers conducting the Project P.A.T.H.S. (Positive Adolescent Training through Holistic Social Programmes) in different years (n = 177 participants in 36 focus groups) was carried out. General qualitative data analyses utilizing intra and interrater reliability techniques were performed. Results showed that the descriptors used to describe the program and the metaphors named by the informants that could stand for the program were generally positive in nature. Program participants also perceived the program to be beneficial to the development of the students in different psychosocial domains. The present study further supports the effectiveness of the Tier 1 Program of the Project P.A.T.H.S. in Hong Kong based on the perspective of the program implementers. PMID:22666139
Vulnerabilities, Influences and Interaction Paths: Failure Data for Integrated System Risk Analysis
NASA Technical Reports Server (NTRS)
Malin, Jane T.; Fleming, Land
2006-01-01
We describe graph-based analysis methods for identifying and analyzing cross-subsystem interaction risks from subsystem connectivity information. By discovering external and remote influences that would be otherwise unexpected, these methods can support better communication among subsystem designers at points of potential conflict and to support design of more dependable and diagnosable systems. These methods identify hazard causes that can impact vulnerable functions or entities if propagated across interaction paths from the hazard source to the vulnerable target. The analysis can also assess combined impacts of And-Or trees of disabling influences. The analysis can use ratings of hazards and vulnerabilities to calculate cumulative measures of the severity and importance. Identification of cross-subsystem hazard-vulnerability pairs and propagation paths across subsystems will increase coverage of hazard and risk analysis and can indicate risk control and protection strategies.
Vulnerabilities, Influences and Interaction Paths: Failure Data for Integrated System Risk Analysis
NASA Technical Reports Server (NTRS)
Malin, Jane T.; Fleming, Land
2006-01-01
We describe graph-based analysis methods for identifying and analyzing cross-subsystem interaction risks from subsystem connectivity information. By discovering external and remote influences that would be otherwise unexpected, these methods can support better communication among subsystem designers at points of potential conflict and to support design of more dependable and diagnosable systems. These methods identify hazard causes that can impact vulnerable functions or entities if propagated across interaction paths from the hazard source to the vulnerable target. The analysis can also assess combined impacts of And-Or trees of disabling influences. The analysis can use ratings of hazards and vulnerabilities to calculate cumulative measures of the severity and importance. Identification of cross-subsystem hazard-vulnerability pairs and propagation paths across subsystems will increase coverage of hazard and risk analysis and can indicate risk control and protection strategies.
Path dependence of J in three numerical examples. [J integral in three crack propagation problems
NASA Technical Reports Server (NTRS)
Karabin, M. E., Jr.; Swedlow, J. L.
1979-01-01
Three cracked geometries are studied with the aid of a new finite element model. The procedure employs a variable singularity at the crack tip that tracks changes in the material response during the loading process. Two of the problems are tension-loaded center-crack panels and the other is a three-point bend specimen. Results usually agree with other numerical and analytical analyses, except the finding that J is path dependent as a substantial plastic zone develops. Credible J values are obtained near the crack tip and J shows a significant increase as the radius of J path increases over two orders of magnitude. Incremental and deformation theories are identical provided the stresses exhibit proportionality found in the far field stresses but not near the tip.
A comparison of NH{sub 3} point monitoring and diode laser based path integrated measurements
Goldstein, N.; Richtsmeier, S.C.; Lee, J.; Bien, F.; Fetzer, G.J.; Groff, K.W.
1994-12-31
Measurements made using two different types of ammonia monitors during a two-month field study in the summer of 1994 are discussed. The first was a diode-laser based open path monitor designed for automated operation in an industrial environment. The second is a monitoring analyzer based on thermal decomposition of ammonia to NO and subsequent analysis by O{sub 3}-NO chemiluminescence. The two monitors provided consistent measurements of ammonia concentration during weeks of continuous unattended operation.
Lemmens, D; Wouters, M; Tempere, J; Foulon, S
2008-07-01
We present a path integral method to derive closed-form solutions for option prices in a stochastic volatility model. The method is explained in detail for the pricing of a plain vanilla option. The flexibility of our approach is demonstrated by extending the realm of closed-form option price formulas to the case where both the volatility and interest rates are stochastic. This flexibility is promising for the treatment of exotic options. Our analytical formulas are tested with numerical Monte Carlo simulations.
NASA Astrophysics Data System (ADS)
Saito, Hiroki
2016-05-01
Motivated by recent experiments [H. Kadau et al., http://doi.org/10.1038/nature16485, Nature (London) 530, 194 (2016); I. Ferrier-Barbut et al., http://arxiv.org/abs/1601.03318, arXiv:1601.03318] and theoretical prediction (F. Wächtler and L. Santos, http://arxiv.org/abs/1601.04501, arXiv:1601.04501), the ground state of a dysprosium Bose-Einstein condensate with strong dipole-dipole interaction is studied by the path-integral Monte Carlo method. It is shown that quantum fluctuation can stabilize the condensate against dipolar collapse.
NASA Astrophysics Data System (ADS)
Lemmens, D.; Wouters, M.; Tempere, J.; Foulon, S.
2008-07-01
We present a path integral method to derive closed-form solutions for option prices in a stochastic volatility model. The method is explained in detail for the pricing of a plain vanilla option. The flexibility of our approach is demonstrated by extending the realm of closed-form option price formulas to the case where both the volatility and interest rates are stochastic. This flexibility is promising for the treatment of exotic options. Our analytical formulas are tested with numerical Monte Carlo simulations.
Ab initio path integral simulation study on 16O/ 18O isotope effect in water and hydronium ion
NASA Astrophysics Data System (ADS)
Tachikawa, Masanori; Shiga, Motoyuki
2005-05-01
An ab initio path integral molecular dynamics simulation has been performed to study the 16O and 18O isotopomers for a water molecule and a hydronium ion at temperature 300 K. The average O-H bond length of H 218O molecule is slightly shorter than that of H 216O molecule, while that of H 318O + is slightly longer than that of H 316O +. For hydronium ions, the Walden inversion of H 318O +, as well as D 316O +, is found to be more restrained than that of H 316O +. The isotope effect in the electronic structure and thermochemical properties for these isotopomers are also shown.
Path integral Monte Carlo approach to the U(1) lattice gauge theory in 2+1 dimensions
NASA Astrophysics Data System (ADS)
Loan, Mushtaq; Brunner, Michael; Sloggett, Clare; Hamer, Chris
2003-08-01
Path integral Monte Carlo simulations have been performed for U(1) lattice gauge theory in 2+1 dimensions on anisotropic lattices. We extract the static quark potential, the string tension and the low-lying “glueball” spectrum. The Euclidean string tension and mass gap decrease exponentially at weak coupling in excellent agreement with the predictions of Polyakov and Göpfert and Mack, but their magnitudes are five times bigger than predicted. Extrapolations are made to the extreme anisotropic or Hamiltonian limit, and comparisons are made with previous estimates obtained in the Hamiltonian formulation.
NASA Astrophysics Data System (ADS)
Kawashima, Yukio; Tachikawa, Masanori
2013-05-01
Ab initio path integral molecular dynamics simulation was performed to understand the nuclear quantum effect on the hydrogen bond of hydrogen malonate anion. Static calculation predicted the proton transfer barrier as 0.12 kcal/mol. Conventional ab initio molecular dynamics simulation at 300 K found proton distribution with a double peak on the proton transfer coordinate. Inclusion of thermal effect alone elongates the hydrogen bond length, which increases the barrier height. Inclusion of nuclear quantum effect washes out this barrier, and distributes a single broad peak in the center. H/D isotope effect on the proton transfer is also discussed.
NASA Astrophysics Data System (ADS)
Yoshikawa, Takehiro; Sugawara, Shuichi; Takayanagi, Toshiyuki; Shiga, Motoyuki; Tachikawa, Masanori
2010-08-01
Full-dimensional path-integral molecular dynamics simulations were performed to determine whether the double proton transfer tautomerization of porphycene is a concerted or a stepwise process. We employed an on-the-fly direct dynamics technique at the semiempirical PM6 method whose parameters were determined so as that the relative energies of the stationary points approximately reproduce previously reported electronic structure calculations. It was found that double proton transfer occurs dominantly through the concerted pathway via the second-order saddle point structure and that contribution of the stepwise mechanism increases with a temperature increase. Nuclear quantum effects play essential roles in determining the proton transfer mechanism.
NASA Astrophysics Data System (ADS)
Kakizaki, Akira; Takayanagi, Toshiyuki; Shiga, Motoyuki
2007-11-01
Path integral molecular dynamics simulations for the H6+ and D6+ cluster cations have been carried out in order to understand the floppy nature of their molecular structure due to quantum-mechanical fluctuation. A full-dimensional analytical potential energy surface for the ground electronic state of H6+ has been developed on the basis of accurate ab initio electronic structure calculations at the CCSD(T)/cc-pVTZ level. It is found that the outer H 2(D 2) nuclei rotate almost freely and that the probability density distributions of the central H 2(D 2) nuclei show strong spatial delocalization.
NASA Astrophysics Data System (ADS)
Müser, Martin H.
2001-04-01
Classical and path integral molecular dynamics (PIMD) simulations are used to study α and β quartz in a large range of temperatures at zero external stress. PIMD account for quantum fluctuations of atomic vibrations, which can modify material properties at temperatures below the Debye temperature. The difference between classical and quantum mechanical results for bond lengths, bond angles, elastic moduli, and some dynamical properties is calculated and comparison to experimental data is done. Only quantum mechanical simulations are able to reproduce the correct thermomechanical properties below room temperature. It is discussed in how far classical and PIMD simulations can be helpful in constructing improved potential energy surfaces for silica.
A kinetic model for voltage-gated ion channels in cell membranes based on the path integral method
NASA Astrophysics Data System (ADS)
Erdem, Rıza; Ekiz, Cesur
2005-04-01
A kinetic model of cell membrane ion channels is proposed based on the path integral method. From the Pauli-type master equations valid on a macroscopic time scale, we derive a first-order differential equation or the kinetic equation which governs temporal evolution of the channel system along the paths of extreme probability. Using known parameters for the batrachotoxin (BTX)-modified sodium channels in squid giant axon, the time dependence of the channel activation and the voltage dependence of the corresponding time constants ( τ) are examined numerically. It is found that the channel activation relaxes to the steady (or equilibrium)-state values for a given membrane potential and the corresponding time constant reaches a maximum at a certain potential and thereafter decreases in magnitude as the membrane potential increases. A qualitative comparison between these results and the results of Hodgkin-Huxley theory, path probability method and thermodynamic models as well as the cut-open axon technique is presented. Good agreement is achieved.
NASA Astrophysics Data System (ADS)
Miura, Shinichi; Okazaki, Susumu
2001-09-01
In this paper, the path integral molecular dynamics (PIMD) method has been extended to employ an efficient approximation of the path action referred to as the pair density matrix approximation. Configurations of the isomorphic classical systems were dynamically sampled by introducing fictitious momenta as in the PIMD based on the standard primitive approximation. The indistinguishability of the particles was handled by a pseudopotential of particle permutation that is an extension of our previous one [J. Chem. Phys. 112, 10 116 (2000)]. As a test of our methodology for Boltzmann statistics, calculations have been performed for liquid helium-4 at 4 K. We found that the PIMD with the pair density matrix approximation dramatically reduced the computational cost to obtain the structural as well as dynamical (using the centroid molecular dynamics approximation) properties at the same level of accuracy as that with the primitive approximation. With respect to the identical particles, we performed the calculation of a bosonic triatomic cluster. Unlike the primitive approximation, the pseudopotential scheme based on the pair density matrix approximation described well the bosonic correlation among the interacting atoms. Convergence with a small number of discretization of the path achieved by this approximation enables us to construct a method of avoiding the problem of the vanishing pseudopotential encountered in the calculations by the primitive approximation.
NASA Astrophysics Data System (ADS)
Janakiraman, Deepika; Sebastian, K. L.
2012-12-01
Lévy flights can be described using a Fokker-Planck equation, which involves a fractional derivative operator in the position coordinate. Such an operator has its natural expression in the Fourier domain. Starting with this, we show that the solution of the equation can be written as a Hamiltonian path integral. Though this has been realized in the literature, the method has not found applications as the path integral appears difficult to evaluate. We show that a method in which one integrates over the position coordinates first, after which integration is performed over the momentum coordinates, can be used to evaluate several path integrals that are of interest. Using this, we evaluate the propagators for (a) free particle, (b) particle subjected to a linear potential, and (c) harmonic potential. In all the three cases, we have obtained results for both overdamped and underdamped cases.
NASA Astrophysics Data System (ADS)
Wendland, D.; Ballenegger, V.; Alastuey, A.
2014-11-01
We compute two- and three-body cluster functions that describe contributions of composite entities, like hydrogen atoms, ions H-, H_2^+, and helium atoms, and also charge-charge and atom-charge interactions, to the equation of state of a hydrogen-helium mixture at low density. A cluster function has the structure of a truncated virial coefficient and behaves, at low temperatures, like a usual partition function for the composite entity. Our path integral Monte Carlo calculations use importance sampling to sample efficiently the cluster partition functions even at low temperatures where bound state contributions dominate. We also employ a new and efficient adaptive discretization scheme that allows one not only to eliminate Coulomb divergencies in discretized path integrals, but also to direct the computational effort where particles are close and thus strongly interacting. The numerical results for the two-body function agree with the analytically known quantum second virial coefficient. The three-body cluster functions are compared at low temperatures with familiar partition functions for composite entities.
Wendland, D.; Ballenegger, V.; Alastuey, A.
2014-11-14
We compute two- and three-body cluster functions that describe contributions of composite entities, like hydrogen atoms, ions H{sup −}, H{sub 2}{sup +}, and helium atoms, and also charge-charge and atom-charge interactions, to the equation of state of a hydrogen-helium mixture at low density. A cluster function has the structure of a truncated virial coefficient and behaves, at low temperatures, like a usual partition function for the composite entity. Our path integral Monte Carlo calculations use importance sampling to sample efficiently the cluster partition functions even at low temperatures where bound state contributions dominate. We also employ a new and efficient adaptive discretization scheme that allows one not only to eliminate Coulomb divergencies in discretized path integrals, but also to direct the computational effort where particles are close and thus strongly interacting. The numerical results for the two-body function agree with the analytically known quantum second virial coefficient. The three-body cluster functions are compared at low temperatures with familiar partition functions for composite entities.
NASA Astrophysics Data System (ADS)
Filinov, V. S.; Fortov, V. E.; Bonitz, M.; Moldabekov, Zh
2015-11-01
The uniform electron gas (UEG) at finite temperature has recently attracted substantial interest due to the experimental progress in the field of warm dense matter. To explain the experimental data accurate theoretical models for high density plasmas are needed which crucially depend on treatment of quantum effects in electron-electron interaction as well as in the interaction of electrons with uniform positive background. To comply with these requirements we have developed the new quantum path integral model of the UEG and present the results of related direct path integral Monte-Carlo (DPIMC) simulations. Contrary to the known in literature approaches treating the electron-background interaction classically our simulations take into account the quantum effects in this interaction. We have observed very good agreement with known in literature results only up to moderate densities when the ratio of the average interparticle distance to the Bohr radius is of order four (rs ≥ 4) and observe deviations for higher densities. At very high electron density (rs ≈ 1) presented in literature approaches as well as our simulations are problematic due to the strong degeneracy of electrons and increasing fermion sign problem.
NASA Technical Reports Server (NTRS)
Bernstein, D. R.; Dashen, R.; Flatte, S. M.
1983-01-01
A theory is developed which describes intensity moments for wave propagation through random media. It is shown using the path integral technique that these moments are significantly different from those of a Rayleigh distribution in certain asymptotic regions. The path integral approach is extended to inhomogeneous, anisotropic media possessing a strong deterministic velocity profile. The behavior of the corrections to Rayleigh statistics is examined, and it is shown that the important characteristics can be attributed to a local micropath focusing function. The correction factor gamma is a micropath focusing parameter defined in terms of medium fluctuations. The value of gamma is calculated for three ocean acoustic experiments, using internal waves as the medium fluctuations. It is found that all three experiments show excellent agreement as to the relative values of the intensity moments. The full curved ray is found to yield results that are significantly different from the straight-line approximations. It is noted that these methods are applicable to a variety of experimental situations, including atmospheric optics and radio waves through plasmas.
NASA Astrophysics Data System (ADS)
Kapila, Vivek; Deymier, Pierre; Runge, Keith
2012-02-01
Warm dense matter (WDM) can be characterized by electron temperatures of a few eV and densities an order of magnitude or more beyond ambient. This regime currently lacks any adequate highly developed class of simulation methods. Recent developments in orbital-free Density Functional Theory (ofDFT) aim to provide such a simulation method, however, little benchmark information is available on temperature and pressure dependence of simple but realistic models in WDM regime. The present work aims to fill this critical gap using the restricted path-integral molecular dynamics (rPIMD) method. Within the discrete path integral representation, electrons are described as harmonic necklaces, while, quantum exchange takes the form of cross linking between electron necklaces. The fermion sign problem is addressed by restricting the density matrix to positive values and a molecular dynamics algorithm is employed to sample phase space. Here, we focus on the behavior of strongly correlated electron plasmas under WDM conditions. We compute the kinetic and potential energies and compare them to those obtained with the ofDFT method.
NASA Astrophysics Data System (ADS)
Runge, Keith; Deymier, Pierre
2013-03-01
Recent progress in orbital-free Density Functional Theory (OF-DFT), particularly with regard to temperature dependent functionals, has promise for the simulation of warm dense matter (WDM) systems. WDM includes systems with densities of an order of magnitude beyond ambient or more and temperatures measured in kilokelvin. A challenge for the development of temperature dependent OF-DFT functionals is the lack of benchmark information with temperature and pressure dependence on simple models under WDM conditions. We present an approach to fill this critical gap using the restricted path-integral molecular dynamics (rPIMD) method. Electrons are described as harmonic necklaces within the discrete path integral representation while quantum exchange takes the form of cross linking between electron necklaces. A molecular dynamics algorithm is used to sample phase space and the fermion sign problem is addressed by restricting the density matrix to positive values. The temperature dependence of kinetic energies for the strongly coupled electron plasma is presented for a number of Wigner-Seitz radii in terms of a fourth order Sommerfeld expansion. Supported by US DoE Grant DE-SC0002139
Wong, Kin-Yiu; Xu, Yuqing; York, Darrin M
2014-06-30
Detailed understandings of the reaction mechanisms of RNA catalysis in various environments can have profound importance for many applications, ranging from the design of new biotechnologies to the unraveling of the evolutionary origin of life. An integral step in the nucleolytic RNA catalysis is self-cleavage of RNA strands by 2'-O-transphosphorylation. Key to elucidating a reaction mechanism is determining the molecular structure and bonding characteristics of transition state. A direct and powerful probe of transition state is measuring isotope effects on biochemical reactions, particularly if we can reproduce isotope effect values from quantum calculations. This article significantly extends the scope of our previous joint experimental and theoretical work in examining isotope effects on enzymatic and nonenzymatic 2'-O-transphosphorylation reaction models that mimic reactions catalyzed by RNA enzymes (ribozymes), and protein enzymes such as ribonuclease A (RNase A). Native reactions are studied, as well as reactions with thio substitutions representing chemical modifications often used in experiments to probe mechanism. Here, we report and compare results from eight levels of electronic-structure calculations for constructing the potential energy surfaces in kinetic and equilibrium isotope effects (KIE and EIE) computations, including a "gold-standard" coupled-cluster level of theory [CCSD(T)]. In addition to the widely used Bigeleisen equation for estimating KIE and EIE values, internuclear anharmonicity and quantum tunneling effects were also computed using our recently developed ab initio path-integral method, that is, automated integration-free path-integral method. The results of this work establish an important set of benchmarks that serve to guide calculations of KIE and EIE for RNA catalysis.
Test-Taker Characteristics and Integrated Speaking Test Performance: A Path-Analytic Study
ERIC Educational Resources Information Center
Huang, Heng-Tsung Danny; Hung, Shao-Ting Alan; Hong, He-Ting Vivian
2016-01-01
This study explored the relationships among language proficiency, two selected test-taker characteristics (i.e., topical knowledge and anxiety), and integrated speaking test performance. Data collection capitalized on three sets of instruments: three integrated tasks derived from TOEFL-iBT preparation materials, the state anxiety inventory created…
Test-Taker Characteristics and Integrated Speaking Test Performance: A Path-Analytic Study
ERIC Educational Resources Information Center
Huang, Heng-Tsung Danny; Hung, Shao-Ting Alan; Hong, He-Ting Vivian
2016-01-01
This study explored the relationships among language proficiency, two selected test-taker characteristics (i.e., topical knowledge and anxiety), and integrated speaking test performance. Data collection capitalized on three sets of instruments: three integrated tasks derived from TOEFL-iBT preparation materials, the state anxiety inventory created…
NASA Astrophysics Data System (ADS)
Filinov, V. S.; Ivanov, Yu. B.; Fortov, V. E.; Bonitz, M.; Levashov, P. R.
2013-03-01
Based on the quasiparticle model of the quark-gluon plasma (QGP), a color quantum path-integral Monte-Carlo (PIMC) method for the calculation of thermodynamic properties and—closely related to the latter—a Wigner dynamics method for calculation of transport properties of the QGP are formulated. The QGP partition function is presented in the form of a color path integral with a new relativistic measure instead of the Gaussian one traditionally used in the Feynman-Wiener path integral. A procedure of sampling color variables according to the SU(3) group Haar measure is developed for integration over the color variable. It is shown that the PIMC method is able to reproduce the lattice QCD equation of state at zero baryon chemical potential at realistic model parameters (i.e., quasiparticle masses and coupling constant) and also yields valuable insight into the internal structure of the QGP. Our results indicate that the QGP reveals quantum liquidlike(rather than gaslike) properties up to the highest considered temperature of 525 MeV. The pair distribution functions clearly reflect the existence of gluon-gluon bound states, i.e., glueballs, at temperatures just above the phase transition, while mesonlike qq¯ bound states are not found. The calculated self-diffusion coefficient agrees well with some estimates of the heavy-quark diffusion constant available from recent lattice data and also with an analysis of heavy-quark quenching in experiments on ultrarelativistic heavy-ion collisions, however, appreciably exceeds other estimates. The lattice and heavy-quark-quenching results on the heavy-quark diffusion are still rather diverse. The obtained results for the shear viscosity are in the range of those deduced from an analysis of the experimental elliptic flow in ultrarelativistic heavy-ions collisions, i.e., in terms the viscosity-to-entropy ratio, 1/4π≲η/S<2.5/4π, in the temperature range from 170 to 440 MeV.
Lugani, Jasleen; Ghosh, Sankalpa; Thyagarajan, K.
2011-06-15
Integrated optical devices are expected to play a promising role in the field of quantum information science and technology. In this paper we propose a scheme for the generation of nondegenerate, copolarized, modal, and path-entangled photons using a directional coupler and an asymmetric Y-coupler geometry in type-0 phase-matched domain-engineered lithium niobate (LN) waveguide. The nonlinearity in LN is tailored in such a way that quasi-phase-matching conditions for two different spontaneous parametric down-conversion processes are obeyed simultaneously, leading to a modal and path-entangled state at the output. Assuming typical values of various parameters, we show, through numerical simulations, that an almost maximally entangled state is achievable over a wide range of waveguide parameters. For the degenerate case, the proposed scheme gives a NOON state for N = 2. The generated entangled photon pairs should have potential applications in quantum information schemes and also in quantum metrology. By appropriate domain engineering and component designing, the idea can be further extended to generate hyperentangled and two-photon multipath-entangled states, which may have further applications in quantum computation protocols.
NASA Astrophysics Data System (ADS)
Distasio, Robert A., Jr.; Santra, Biswajit; Ko, Hsin-Yu; Car, Roberto
2014-03-01
In this work, we report highly accurate ab initio path-integral molecular dynamics (AI-PIMD) simulations on liquid water at ambient conditions utilizing the recently developed PBE0+vdW(SC) exchange-correlation functional, which accounts for exact exchange and a self-consistent pairwise treatment of van der Waals (vdW) or dispersion interactions, combined with nuclear quantum effects (via the colored-noise generalized Langevin equation). The importance of each of these effects in the theoretical prediction of the structure of liquid water will be demonstrated by a detailed comparative analysis of the predicted and experimental oxygen-oxygen (O-O), oxygen-hydrogen (O-H), and hydrogen-hydrogen (H-H) radial distribution functions as well as other structural properties. In addition, we will discuss the theoretically obtained proton momentum distribution, computed using the recently developed Feynman path formulation, in light of the experimental deep inelastic neutron scattering (DINS) measurements. DOE: DE-SC0008626, DOE: DE-SC0005180.
The polarization compass dominates over idiothetic cues in path integration of desert ants.
Lebhardt, Fleur; Koch, Julja; Ronacher, Bernhard
2012-02-01
Desert ants, Cataglyphis, use the sky's pattern of polarized light as a compass reference for navigation. However, they do not fully exploit the complexity of this pattern, rather - as proposed previously - they assess their walking direction by means of an approximate solution based on a simplified internal template. Approximate rules are error-prone. We therefore asked whether the ants use additional cues to improve the accuracy of directional decisions, and focused on 'idiothetic' cues, i.e. cues based on information from proprioceptors. We trained ants in a channel system that was covered with a polarization filter, providing only a single e-vector direction as a directional 'celestial' cue. Then we observed their homebound runs on a test field, allowing full view of the sky. In crucial experiments, the ants were exposed to a cue conflict, in which sky compass and idiothetic information disagreed, by training them in a straight channel that provided a change in e-vector direction. The results indicated that the polarization information completely dominates over idiothetic cues. Two path segments with different e-vector orientations are combined linearly to a summed home vector. Our data provide additional evidence that Cataglyphis uses a simplified internal template to derive directional information from the sky's polarization pattern.
Simulation of thermal ionization in a dense helium plasma by the Feynman path integral method
NASA Astrophysics Data System (ADS)
Shevkunov, S. V.
2011-04-01
The region of equilibrium states is studied where the quantum nature of the electron component and a strong nonideality of a plasma play a key role. The problem of negative signs in the calculation of equilibrium averages a system of indistinguishable quantum particles with a spin is solved in the macroscopic limit. It is demonstrated that the calculation can be conducted up to a numerical result. The complete set of symmetrized basis wave functions is constructed based on the Young symmetry operators. The combinatorial weight coefficients of the states corresponding to different graphs of connected Feynman paths in multiparticle systems are calculated by the method of random walk over permutation classes. The kinetic energy is calculated using a viral estimator at a finite pressure in a statistical ensemble with flexible boundaries. Based on the methods developed in the paper, the computer simulation is performed for a dense helium plasma in the temperature range from 30000 to 40000 K. The equation of state, internal energy, ionization degree, and structural characteristic of the plasma are calculated in terms of spatial correlation functions. The parameters of a pseudopotential plasma model are estimated.
The Regional University: Paths of Integration in the Framework of the Bologna Process
ERIC Educational Resources Information Center
Lazarev, G.; Martynenko, O.
2006-01-01
The development of international systems of education is opening the way to accomplish tasks in the sphere of higher education that are common to the world community. The Bologna Process, in the framework of which the educational systems of Europe are becoming integrated, makes it possible for Russia to make a choice of the forms of its…
NASA Astrophysics Data System (ADS)
Gratton, Steven
2011-09-01
In this paper we present a path integral formulation of stochastic inflation. Volume weighting can be naturally implemented from this new perspective in a very straightforward way when compared to conventional Langevin approaches. With an in-depth study of inflation in a quartic potential, we investigate how the inflaton evolves and how inflation typically ends both with and without volume weighting. The calculation can be carried to times beyond those accessible to conventional Fokker-Planck approaches. Perhaps unexpectedly, complex histories sometimes emerge with volume weighting. The reward for this excursion into the complex plane is an insight into how volume-weighted inflation both loses memory of initial conditions and ends via slow roll. The slow-roll end of inflation mitigates certain “Youngness Paradox”-type criticisms of the volume-weighted paradigm. Thus it is perhaps time to rehabilitate proper-time volume weighting as a viable measure for answering at least some interesting cosmological questions.